UNIVERSITY  OF  CALIFORNIA 
LOS  ANGELES 


COMPRESSED  AIR 


COMPRESSED  AIR 


A  TREATISE  ON  THE  PRODUCTION 

TRANSMISSION  AND  USE  OF 

COMPRESSED  AIR 


BY 
THEODORE  SIMONS,  E.  M.,  C.  E. 

PROFESSOR  OF  MINING  ENGINEERING,  UNIVERSITY  OF  MONTANA. 

SCHOOL  OF  MINES;  MEMBER  AMERICAN  INSTITUTE  OF 

MINING  AND  METALLURGICAL  ENGINEERS 


SECOND  EDITION 
FIFTH  IMPRESSION 


McGRAW-HILL  BOOK  COMPANY,  INC. 

NEW     YORK    AND     LONDON 
1921 


COPYRIGHT,  1914,  1921,  BY  THE 
McGRAW-HiLL  BOOK  COMPANY,  INC. 


PREFACE  TO  SECOND  EDITION 

In  preparing  a  second  edition  of  this  book,  its  character  as  an 
elementary  treatise  on  the  principles  of  Compressed  Air  has 
been  maintained  throughout.  To  bring  the  subject  up-to-date, 
however,  the  greater  portion  of  the  chapter  on  Transmission  has 
been  re-written.  Modern  formulas  were  introduced  with  ex- 
amples of  their  application.  The  important  effect  of  altitude 
differences  on  Compressed  Air  installations  has  been  illustrated 
by  reference  to  new  equations  in  Article  4  and  by  the  example 
under  Article  97.  A  new  Table  VIII,  containing  the  principal 
Compressed  Air  formulas  was  substituted  for  the  old  table  that 
has  become  superfluous.  The  obsolete  Hurricane  valve  in 
Article  147  has  been  replaced  by  a  description  of  the  modern 
Ingersoll-Rogler  valve. 

Altogether,  a  general  revision  of  the  original  text  and  the 
addition  of  new  material  brings  the  second  edition  of  the  book 
abreast  of  modern  theory  and  practice. 

THEODORE  SIMONS. 

BUTTE,  MONTANA, 
December,  1920. 


Library 
TJ 


ESGI 


PREFACE  TO  FIRST  EDITION 

This  treatise  is  intended  to  give  the  student  and  the  general 
reader  such  an  insight  into  the  natural  laws  and  physical  prin- 
ciples underlying  the  production,  transmission  and  use  of  com- 
pressed air,  as  shall  enable  him  to  comprehend  the  operation  of 
the  various  appliances  employed  for  this  purpose  and  to  judge 
of  their  merit. 

No  attempt  has  been  made  to  present  in  this  book  an  extensive 
description  of  all  the  existing  types  of  compressors  or  of  the  count- 
less appliances  using  compressed  air.  The  author's  chief  aim 
was  to  provide  the  student,  who  is  interested  in  technical  ques- 
tions concerning  the  operation  as  well  as  the  construction  of 
compressors  and  air  engines,  with  a  background  of  understand- 
ing that  will  enable  him,  not  only  to  solve  the  many  theoretical 
problems  connected  therewith,  but  to  make  independent  research 
into  the  seemingly  unlimited  possibilities  of  compressed  air. 
The  territory  still  unexplored  is  vast  and  full  of  promises  to  the 
intrepid  explorer  who  enters  the  field  with  a  thorough  knowledge 
of  all  the  truths  discovered,  as  well  as  the  pitfalls  encountered, 
by  those  who  have  gone  before  him. 

The  numerous,  carefully  selected  problems  constitute  what 
the  author  believes  to  be  one  of  the  strong  features  of  this  book. 
If  ever  any  doubt  lingers  in  the  student's  mind  as  to  the  mean- 
ing of  certain  principles  or  laws  presented  in  the  text  and  their 
practical  application,  a  numerical  problem  will,  as  a  rule,  re- 
move the  doubt  and  make  clear  the  meaning.  Moreover,  such 
problems  make  the  student  familiar  with  actual  quantities,  never 
revealed  by  mere  formulas;  quantities  which  are  often  startling 
to  the  uninitiated  and  impress  him  with  the  practical  value  of 
such  formulas  more  forcibly  then  the  mere  text  can  do. 

The  author  has  endeavored  to  bring  the  work  well  within 
the  comprehension  of  the  average  technical  student  who  has  a 
sound  knowledge  of  the  elements  of  algebra,  physics  and  me- 
chanics. Higher  mathematics  were  used  sparingly  and  only 
when  they  led  to  a  simpler  solution  of  certain  problems.  To  the 
advanced  reader  some  of  the  deductions  contained  in  the  book 

vii 


viii  PREFACE 

may  appear  unnecessarily  lengthy.  It  has  been  the  writer's 
experience,  however,  that  many  of  the  difficulties  encountered 
by  students  arise  from  a  misunderstanding  of  facts  which,  al- 
though perfectly  obvious  to  one  who  has  mastered  the  subject, 
remain  nevertheless  obscure  to  the  beginner  unless  explained 
from  various  points  of  view  and  by  analogy  with  facts  already 
familiar  to  him. 

In  preparing  this  treatise  the  writer  has  made  free  use  of  the 
rather  scattered  and  by  no  means  voluminous  literature  on  the 
subject  of  compressed  air.  His  debt  to  all  who  have  labored  in 
this  field  before  him  can  hardly  be  acknowledged  adequately 
by  the  mere  mentioning  of  their  names.  He  has  therefore  re- 
frained from  referring  in  the  text  to  such  names  but  wishes  to 
express  in  this  preface  his  gratitude  to  all  authors  and  investi- 
gators from  whose  writings  he  has  drawn  both  inspiration  and 
information. 

Throughout  the  preparation  of  this  work  the  author  had  the 
untiring  assistance  of  President  C.  H.  Bowman  of  the  Montana 
State  School  of  Mines,  whose  constructive  criticism  and  sugges- 
tions, based  on  a  vast  theoretical  knowledge  and  practical  ex- 
perience, were  of  inestimable  value.  To  him  the  author  is  in- 
debted to  an  extent  that  the  mere  mentioning  of  the  fact  can 
scarcely  requite. 

For  permission  to  use  diagrams,  illustrations,  tables  and  other 
data,  contained  in  the  bulletins  of  manufacturers,  the  author  is 
indebted  to  the  following  firms:  Allis  Chalmers  Company, 
Ingersoll  Rand  Company,  Nordberg  Manufacturing  Company, 
Norwalk  Iron  Works  Company,  Sullivan  Machinery  Com- 
pany, The  Laidlaw-Dunn-Gordon  Company  and  Union  Steam 
Company. 

THEODORE  SIMONS. 

,  MONTANA, 
April,  1914. 


CONTENTS 


PAGE 
PREFACE .  .  v 


PART  I 
THE  PRODUCTION  OF  COMPRESSED  AIR 

CHAPTER  I 

THE  PHYSICAL  PROPERTIES  OF  AIR.     DEFINITION  OF  TERMS  USED  IN 
DISCUSSING  COMPRESSED-AIR  PROBLEMS 

1.  Composition  of  air. 

2.  Weight  of  air. 

3.  Atmospheric  pressure. 

4.  Formulas  for  calculation  of  atmospheric  pressure  and  altitudes. 

5.  General  effect  of  heat  on  air. 

6.  Specific  heat  and  the  B.T.U. 

7.  Specific  heat  of  air  at  constant  volume. 

8.  Specific  heat  of  air  at  constant  pressure. 

9.  Absolute  zero. 

10.  Absolute  temperature. 

11.  Gage  and  absolute  pressure. 

12.  Free  air. 

13.  Isothermal  compression  and  expansion. 

14.  Adiabatic  compression  and  expansion. 


CHAPTER  II 

BEHAVIOR   OF  AIR  UNDERGOING  COMPRESSION  AND  UNDER  THE  APPLI- 
CATION OF  HEAT 

15.  Boyle's  or  Mariotte's  law. 

16.  Boyle's  or  Mariotte's  second  statement. 

17.  Charles'  or  Gay  Lussac's  law. 

18.  Charles'  or  Gay  Lussac's  second  statement. 

19.  Charles'  or  Gay  Lussac's  third  statement. 

20.  Boyle's  and  Charles'  laws  combined. 

21.  Weight  of  equal  volumes  of  air  at  constant  pressure  and  vary- 

ing temperature. 

22.  Weight  of  equal  volumes  of  air  at  constant  temperature  and 

varying  pressure. 

23.  Weight  of  one  cubic  foot  of  air  at  atmospheric  pressure  and  at 

any  temperature. 

24.  Weight  of  one  cubic  foot  of  air  a,t  any  absolute  pressure  and 

any  absolute  temperature. 
24a.  Application  of  weight-formulas  to  altitudes. 

ix 


x  CONTENTS 

CHAPTER  III 

PAGE 

THE  COMPRESSION  OF  AIR  IN  AIR  COMPRESSORS 14 

25.  Air  cylinders  of  a  compressor. 

26.  Water-jackets. 

27.  Inlet  and  discharge  valves  in  general. 

28.  Analysis  of  single-stage  compression. 

29.  Receiver  pressure. 

CHAPTER  IV 

THEORY  OF  AIR  COMPRESSION -17 

30.  Theory  of  isothermal  compression. 

31.  Graphical  illustration  of  isothermal  compression. 

32.  Construction  of  isothermal  compression  curve. 

33.  Work  of  isothermal,  single-stage  compression  and  delivery. 

34.  Net  work  per  stroke,  isothermal  compression. 

35.  Net  work,  formula. 

36.  Mean  gage  pressure,  isothermal  compression  and  delivery. 

37.  Horse-power,  isothermal,  single-stage  compression  and  delivery. 

38.  Isothermal  compression  not  attainable  in  practice. 

39.  Isothermal  expansion  formulas. 

40.  Theory  of  adiabatic  compression. 

41.  Relation  between  temperature,  volume  and  pressure  in  adia- 

batic compression  and  expansion. 

41a.  Law  of  thermodynamics  applied  to  adiabatic  compression 
and  expansion. 

42.  Graphical  illustration,  adiabatic  compression. 

43.  Construction  of  adiabatic  compression  curve. 

44.  Work  of  adiabatic,  single-stage  compression  and  delivery. 

45.  Net  work  per  stroke. 

46.  Mean  gage  pressure,  adiabatic,  single-stage  compression 

and  delivery. 

47.  Horse-power,  adiabatic,  single-stage  compression  and  delivery. 

48.  Horse-power  in  terms  of  weight  and  temperature. 

49.  Relation  between  final  pressure  and  power  required  to  compress 

to  that  pressure. 

50.  Modified  power  values  for  practical  computations. 

CHAPTER  V 

CLEARANCE,  VOLUMETRIC  EFFICIENCY,  CAPACITY,  SPEED,  MECHANICAL 

EFFICIENCY   OF  COMPRESSORS 38 

51.  Clearance  explained. 

52.  Losses  due  to  clearance. 

53.  Volumetric  efficiency  of  a  compressor. 

54.  Capacity  of  a  compressor. 

55.  Speed  of  a  compressor. 

56.  Mechanical  efficiency  of  a  compressor. 

CHAPTER  VI 

TWO-STAGE  AND  MULTI-STAGE  COMPRESSION,   ALSO  KNOWN  AS  COM- 
POUND COMPRESSION 43 

57.  Theory  of  compound  or  multi-stage  compression. 

58.  Analysis  of  two-stage  compression. 

59.  Ratio  of  compound  compression. 

60.  Ratio  for  two-stage  compression. 

61.  Ratio  for  three-stage  compression. 

62.  Ratio  for  four-stage  compression. 


CONTENTS  xi 

PAGE 

63.  Cylinder  diameters  of  compound  compressors. 

64.  Cylinder  diameters  of  two-stage  compressors. 

65.  Cylinder  diameters  of  three-stage  compressors. 

66.  Cylinder  diameters  of  four-stage  compressors. 

67.  Volumetric  efficiency  of  compound  compressors. 

68.  Horse-power,  two-stage  compression  and  delivery. 

69.  Horse-power  formula,  two-stage  compression  and  delivery. 

70.  Horse-power  formula,  three-stage  compression  and  delivery. 

71.  Horse-power  formula,  four-stage  compression  and  delivery. 

72.  Mean  gage  pressure,  two-stage  compression  and  delivery. 

73.  Mean  gage  pressure,  three-stage  compression  and  delivery. 
73a.  Final  volumes  and  temperatures — stage  compression. 

74.  Modified  power  values  for  practical  problems. 

75.  Advantages  of  compound  compression. 

76.  When  to  use  compound  compression. 

CHAPTER  VII 

EFFECT  OF  ALTITUDE  ON  AIR  COMPRESSION 60 

77.  Volumetric  efficiency  at  altitudes. 

78.  Multipliers  for  altitude  computations. 

79.  Power  required  for  compression  at  altitudes. 

80.  Stage  compression  at  high  altitudes. 

81.  Advantage  of  stage  compression  at  altitudes. 

CHAPTER  VIII 

THE   COMPRESSED  AIR  INDICATOR  CARD 64 

82.  Air  cards,  explanation,  description  and  interpretation. 

83.  Air  card  of  single-stage  compressor. 

84.  Air  card  of  two-stage  compressor. 

85.  Air  card  of  two-stage  Nordberg  compressor. 

CHAPTER  IX 

COOLING  WATER  REQUIRED  IN  COMPRESSION;  EFFICIENCY  OF  COM- 
PRESSOR PLANT;  AIR-COMPRESSOR  EXPLOSIONS 71 

86.  Amount  of  cooling  water  required  in  compression. 

87.  Efficiency  of  a  compressor  plant. 

88.  Compressor  explosions. 

89.  Dangerous  effect  of  throttling  devices. 

90.  Prevention  of  explosions. 


PART  II 
THE  TRANSMISSION  OF  COMPRESSED  AIR 

CHAPTER  X 

TRANSMISSION  OF  COMPRESSED  AIR 85 

91.  Conveyance  of  compressed  air  in  iron  pipes. 

92.  Laws  governing  flow  of  compressed  air  in  iron  pipes. 

93.  Loss  of  pressure  or  head  in  air  transmission. 

94.  Loss  of  power  in  air  transmission. 


xii  CONTENTS 

CHAPTER  XI 

PAGE 

DIMENSIONS  OF  PIPE  LINES  FOK  CONVEYING  COMPRESSED  Am. 

95.  Dimensions  of  pipe  line  in  general. 

96.  Formulas  for  pipe  line  computations. 

97.  Effect  of  altitude  on  air  transmission. 

98.  Dimensions  of  branch  pipes. 

99.  Effect  of  bends  and  elbows  in  pipe  line. 

100.  Velocity  of  air  in  pipe  line. 

lOOa.  The  planning  of  a  transmission  line. 

101.  Pipe  line  efficiency. 

lOla.  R6sum6  of  pipe  line  computations. 

102.  Effect  of  altitude  on  pipe  line  efficiency. 

103.  Final  dimensions  of  pipe  lines. 

104.  Pipe  line  construction. 

105.  Flow  of  compressed  air  from  an  orifice. 

PART  III 
THE  USE  OF  COMPRESSED  AIR 

CHAPTER  XII 

THEORY  OF  AIR  ENGINES •   105 

106.  Compressed  air  to  drive  engines. 

107.  Compressed  air  used  at  full  pressure. 

108.  Work  performed  by  engines  using  air  at  full  pressure 

109.  Efficiency  of  engines  using  air  at  full  pressure. 

110.  Work  of  air  used  with  complete  adiabatic  expansion. 

111.  Horse-power  developed  by  air  used  with  complete  expansion. 

112.  Complete  expansion  not  practicable 

113.  Work  of  air  used  with  partial  expansion. 

114.  Mean  gage  pressure  partial  expansion. 

115.  Horse-power,  partial  expansion. 

116.  Modified  power  values  for  practical  computations. 

CHAPTER  XIII 

EFFECT  OF  Loss  OF  HEAT,  GENERATED  DURING  COMPRESSION,  ON  THE 
ULTIMATE  USEFUL  ENERGY  RESIDING  IN  A  GIVEN  QUANTITY 
OF  COMPRESSED  AIR 113 

117.  Effect  of  heat  loss  on  energy  in  air. 
117a.  Determination  of  the  value  of  "n". 

CHAPTER  XIV 

INTERNAL  OR  INTRINSIC  ENERGY  OF  AIR 121 

118.  Internal  or  intrinsic  energy  of  air. 

119.  Intrinsic  energy  of  atmospheric  air  at  60°  Fahr. 

120.  Intrinsic  energy  of  air  at  100  Ib.  gage  and  at  60°  Fahr. 

CHAPTER  XV 

THE  EFFICIENCY  OF  A  COMPRESSED-AIR  SYSTEM 124 

CHAPTER  XVI 

REHEATING  OF  COMPRESSED  AIR 126 

122.  Reheating  of  compressed  air. 

123.  Sullivan  air  reheater. 

124.  Sergeant  air  reheater. 

125.  Other  reheaters. 


CONTENTS  xiii 

PART  IV 
AIR  COMPRESSORS  AND  ACCESSORIES 

CHAPTER  XVII 

PAGE 
EXAMPLES  OF  MODERN  AIR-COMPRESSORS  OP  THE  RECIPROCATING  TYPE.  132 

126.  Examples  of  modern  air  compressors. 

127.  Outline  diagram  of  steam-driven  compressors. 

128.  Operation  of  steam-driven,  straight-line  compressors. 

129.  Sullivan  straight-line,  steam-driven,  single-stage  compressor. 

130.  Sullivan  straight-line,  steam-driven,  two-stage  compressor. 

131.  Operation  of  steam-driven  duplex  compressors. 
131a.  Disadvantages  of  duplex  compressors. 

132.  Laidlaw-Dunn-Gordon  duplex,  steam-driven,  single-stage  com- 

pressor. 

133.  Ingersoll-Rand  duplex,  steam-driven,  two-stage  compressor. 

134.  Allis-Chalmers  duplex,  steam-driven,  two-stage  compressor. 

135.  Other  types  of  steam-driven  compressors. 

136.  Power-driven  compressors. 

137.  Belt^driven  compared  with  steam-driven  compressors. 

138.  Norwalk  belt-driven  two-stage  compressor. 

139.  Norwalk  compressor  with  direct  water-wheel  drive. 

140.  Electrically-operated  compressors. 

141.  Nordberg  electrically-driven,  geared  two-stage  compressor. 

142.  Ingersoll-Rand  direct-connected,  electrically-driven  two-stage 

compressor. 

CHAPTER  XVIII 

IMPORTANT  MECHANICAL  FEATURES  OF  AIR  COMPRESSORS T48 

143.  Important  mechanical  features  of  air  compressors. 

144.  Inlet  valves  in  general. 

145.  Poppet  inlet  valves. 

146.  Inlet  valves  of  the  Corliss  type. 

147.  Ingersoll-Rogler  valve. 

148.  Discharge  valves  in  general. 

149.  Poppet  discharge  valves. 

150.  Mechanically  moved  discharge  valves. 

151.  Allis-Chalmers  mechanically  moved  discharge  valve. 

152.  Nordberg  mechanically  moved  discharge  valve. 

153.  Corliss  discharge  valves  not  always  applicable. 

154.  Intercooler. 

155.  Design  of  inter-cooler. 

CHAPTER  XIX 

COMPRESSOR  ACCESSORIES 155 

156.  Compressor  accessories. 

157.  Automatic  regulators. 

158.  Air  cylinders  unloaders. 

159.  Combined  speed-governor  and  air-pressure  regulator. 

160.  Ingersoll-Rand  regulator. 

161.  Air  receivers. 

162.  After-coolers. 

APPENDIX 

TABLES  I  TO  IX 161 

INDEX..  .    169 


PART  1 

THE  PRODUCTION  OF  COMPRESSED  AIR 


COMPRESSED  AIR 


CHAPTER  I 

THE    PHYSICAL    PROPERTIES     OF    AIR.       DEFINITION    OF 

TERMS  USED   IN  THE  DISCUSSION   OF   COMPRESSED 

AIR  PROBLEMS 

1.  Composition  of  Air. — Air  is  chiefly  composed  of  the  ele- 
ments oxygen  and  nitrogen.     By  weight  the  proportions  are 
about  23  parts  of  oxygen  and  77  Darts  of  nitrogen.     By  volume 
the  proportions  are  about  21  parts  of  oxygen  and  79  parts  of 
nitrogen. 

2.  Weigit  of  Air. — By  actual  measurement  it  has  been  found 
that  1  cu.  ft.  of  air  at  atmospheric  pressure  at  sea  level  and  at 
60°  Fahr.  weighs  0.0764  Ib.     Since  the  density  of  air  changes 
with  the  pressure  and  with  the  temperature,  it  follows  that  the 
weight  of  a  given  volume  of  air  varies  with  pressure  and  tem- 
perature.    How  this  weight  can  be  computed  when  pressure  and 
temperature  are  known  is  shown  in  Articles  21  to  24. 

3.  Atmospheric  Pressure. — Since  air  has  weight,  it  is  evident 
that  the  enormous  quantities  of  air  that  constitute  the  atmos- 
phere must  exert  a  considerable  pressure  upon  the  earth. 

By  experiment  the  atmospheric  pressure  at  sea  level,  with 
the  barometer  at  30  in.  and  a  temperature  of  32°  Fahr.,  has  been 
found  to  average  14.7  Ib.  per  square  inch  above  vacuum. 

4.  Air  Pressures  at  Varying  Altitudes  and  Temperatures.— 
The  solving  of  many  compressed-air  problems  requires  a  knowl- 
edge of  the  pressure  at  any  point  of  a  vertical  column  of  free  or 
compressed  air.     Without  havir.g  recourse  to  actual  measure- 
ments, these  pressures  may  be  calculated  as  follows: 

Let  Fig.  1A  represent  an  air  column  having  a  base  1  sq.  in.  in 
area  and  a  height  of  h  feet. 

1 


2  COMPRESSED  AIR 

LetPiandP2  =  absolute  pressures  per  square  inch  at  bottom 

and  at  top  of  column,  respectively. 
-p2  px  =  absolute  pressure  at  a  point  x  ft. 

above    bottom,    in    pounds    per 
Px  square  inch. 

wx  =  weight    in    pounds   of   one  cubic 

foot  of  air  at  point  x. 
Pa  =  atmospheric  pressure  at  sea  level 

(14.7  lb.). 

Wa  =  weight   in    pounds   of  one   cubic 
-p<  foot  of  atmospheric  air  at  sea  level 

and  at  an  absolute  temperature 
FIG.  la.  „, 

Then  the  absolute  pressure  at  a  point  dh  ft.  below  x  will  be 

Px-\-dPx  lb.  per  sq.  in. 

in  which        dPx  =  weight  in  pounds  of  shaded  air  column. 
But  dPx  =  TTTT  dhwx  lb. 


whence 


From  Art.  22 

Wa       Pa 
Px 


(1) 


LJ 

whence  wx  =  wa~         Introducing  in  (1)  gives 


whence 


„    f^K=144Palo       Pi 

Vp, 


(2) 


From  Art  22  the  weight  of  one  cubic  foot  of  atmospheric  air  at 
sea  level  and  at  an  absolute  temperature  Ta  is 
39.804 


Ta 


lb. 


18) 


Introducing  (3)  in  (2)  and  using  common  logarithms,  gives 
14  IT 


whence       log  P2  =  log  PI  — 


122.4  (degree  F.+461) 


(4) 


THE  PHYSICAL  PROPERTIES  OF  AIR  2a 

For  an  average  temperature  of  60°  Fahr.  equation  (4)  becomes  : 

log  P2  =  log  Pi-  0.0000157/1  (5) 

whence  log  PI  =  log  P2+0.0000157/i  (6) 

"- 


Example  1.  —  Atmospheric  pressure  PI  at  sea  level  is  14.7  Ib.  What 
is  atmospheric  pressure  P2  at  an  elevation  of  5000  ft.  above  sea  level 
and  at  a  temperature  of  60°  Fahr.? 

log  P2  =  log  14.7-          500° 


122.4(60+461) 
P8  =12.27  Ib.  per.  sq.  in. 

Example  2.  —  By  barometric  observation  the  atmospheric  pressure 
at  a  certain  mine  was  found  to  be  11.24  Ib.  per  sq.  in.  Average  tem- 
perature 60°  Fahr.  What  is  the  elevation  of  the  mine  above  sea  level? 

From  equation  (7) 


h  =  6370  log  =  7400  ft. 


Example  3.  —  A  compressor  at  a  line,  located  5500  ft.  above  sea  level, 
furnishes  compressed  air  for  air-drills  at  the  bottom  of  a  shaft  2800  ft. 
deep.  A  pressure  gage  in  the  pipe  line,  near  the  shaft  bottom  reads 
60  Ib.,  when  the  air  is  not  moving. 

(a)  What  is  the  absolute  pressure  corresponding  to  this  gage  pressure? 

(6)  What  should  be  the  reading  of  a  pressure-gage  in  the  pipe  line 
at  the  collar  of  the  shaft  and  at  the  same  instant? 

Solution  (a).  Elevation  of  shaft  bottom  above  sea  level  is  5500  — 
2850  =  2650  ft. 

Atmospheric  pressure  at  shaft  bottom 


=  log  14.7-0.0000157X2650 
whence          P265o  =  13.36  Ib. 

Added  to  60  Ib.  gives  absolute  pressure  of  compressed  air  at  shaft 
bottom 

P!  =  60+  13.36  =  73.36  Ib.  abs. 


25  COMPRESSED  AIR 

Solution  (fc).     Atmospheric  pressure  at  shaft  collar: 

logP55oo  =  log  14.7-0.0000157X5500 
whence  P5500  =  12.05  Ib. 

Absolute  pressure  of  compressed  air  at  shaft  collar: 

log  P2  =  log  73.36-O.C000157X2850 
whence       P2=66.2  Ib.  abs. 

Gage  pressure  66.20-12.05  =  54.15  Ib.  gage. 

In  well-regulated  practical  operations  such  readings  are  taken 
frequently  and  at  various  points  in  the  transmission  line.  A 
marked  discrepancy  between  the  actual  and  the  computed 
readings  indicates  trouble  in  the  pipe  line  such  as  leaks  or  care- 
less waste  of  air.  The  cause  of  the  discrepancy  is  then  traced 
to  its  source  and  the  proper  remedies  are  applied  before  much 
harm  is  done. 

5.  General  Effect  of  Heat  on  Air. — Heat  has  a  tendency  to 
increase  the  volume  of  air,  that  is,  to  expand  it.  If  air  at  out- 
side temperature  is  confined  within  a  closed  cylinder,  and  then 
heated,  the  result  of  this  tendency  to  expand  may  be  two-fold : 

1.  If  the  cylinder  is  tightly  closed  at  both  ends,  and  if  the 
walls  are  strong  enough  to  resist  deformation,  the  volume  of  air 
will  remain  constant  and  its  pressure  will  increase. 

2.  If  in  the  upper  end  of  the  cylinder  we  insert  a  piston  which 
is  free  to  move  in  the  cylinder  and  has  a  certain  weight,  it  will 
descend  in  the  air-filled  cylinder  until  its  weight  is  balanced  by 
the  pressure  of  the  confined  air. 

If  now  the  air  in  this  cylinder  is  heated,  it  expands  and  the 
piston  will  start  upward,  and  will  stop  when  the  expansion  has 
ceased;  in  this  case,  the  load  of  the  piston  and  consequently  the 
pressure  of  the  air  have  remained  the  same  as  before  heating, 
but  the  volume  has  increased. 

The  effect  of  heat  upon  the  air  in  the  cylinder  is,  therefore,  in 
the  first  case,  to  increase  its  pressure  under  constant  volume; 
and  in  the  second  case,  to  increase  the  volume  under  constant 
pressure. 

Reversely,  if  we  '-ake  a  closed  cylinder  full  of  hot  air  and  allow 


THE  PHYSICAL  PROPERTIES  OF  AIR  3 

it  to  cool,  the  volume  of  this  air  will,  of  course,  remain  the  same, 
but  its  pressure  will  fall  gradually,  until  it  becomes  the  same  as 
it  was  before  heating. 

In  a  similar  way,  if  we  allow  the  heated  air  in  the  cylinder 
with  its  piston  to  cool,  the  volume  of  air  confined  under  the  piston 
will  shrink,  and  the  piston  will  gradually  descend  to  the  point 
where  it  was  before  the  air  was  heated,  the  pressure,  of  course, 
remaining  constant. 

The  effect  of  abstracting  heat  from  the  air  in  the  cylinder  is, 
therefore,  in  the  first  case,  to  decrease  the  pressure  under  con- 
stant volume;  and  in  the  second  case,  to  decrease  the  volume 
under  constant  pressure. 

6.  Specific  Heat  and  The  British  Thermal  Unit.— The  specific 
heat  of  a  body  is  the  ratio  between  the  amount  of  heat  required 
to  raise  the  temperature  of  that  body  1  degree  and  that  required 
to  raise  the  temperature  of  an  equal  mass  of  water  1  degree. 

In  engineering  problems  the  British  Thermal  Unit  (B.T.U.) 
is  usually  employed  as  the  unit  of  heat.  It  is  the  quantity  of 
heat  required  to  raise  the  temperature  of  1  Ib.  of  water  1°  Fahr. 
Thus,  the  specific  heat  of  water  is  1,  and  the  specific  heat  of  any 
substance  is  the  number  of  B.T.U. 'a  required  to  raise  the  tem- 
perature of  1  Ib.  of  that  substance  1°  Fahr. 

By  a  law  of  thermodynamics,  heat  and  mechanical  energy 
are  mutually  convertible,  and  heat  requires  for  its  production, 
and  produces  by  its  consumption,  a  definite  amount  of  work  for 
each  thermal  unit. 

The  mechanical  equivalent  of  the  British  Thermal  Unit  has 
been  found  to  be  very  close  to  778  ft.-lb.  This  value  will  be 
used  throughout  this  treatise. 

Thus:  1  B.T.U.  =  778  ft.-lb. 

7.  Specific  Heat  of  Air  at  Constant  Volume.— If  heat  is  applied 
to  air  contained  in  a  closed  vessel,  the  air  is  said  to  be  heated  under 
constant  volume.     In  this  case  the  number  of  heat  units  required 
to  raise  the  temperature  of  1  Ib.  of  air  by  1°  Fahr.  is  the  specific 
heat  of  air  at  constant  volume. 

Expressed  in  B.T.U.'s  it  is:     C*  =  0.1689  B.T.U.'s. 
Expressed  in  foot-pounds  it  is:     Kv  =  Cv X778  =  131.6  ft.-lb. 

8.  Specific  Heat  of  Air  at  Constant  Pressure. — If  heat  is  applied 
to  air  in  a  cylinder  having  a  movable  piston  under  a  constant 


4  COMPRESSED  AIR 

external  pressure,  the  volume  increases,  and  therefore  work  is 
done  in  pushing  the  piston  out  against  the  external  pressure. 
The  number  of  heat  units  required  in  this  case  to  raise  the  tem- 
perature of  1  Ib.  of  air  by  1°  Fahr.  is  the  specific  heat  of  air  at 
constant  pressure. 

Expressed  in  B.T.U.'s  it  is:     Cp  =  0.2375  B.T.U.'s. 
Expressed  in  foot-pounds  it  is:     Kp  =  CPX 778  =  184.8  ft.-lb. 

Cp  is  greater  than  C,  owing  to  the  extra  heat  required  to  do  the 
work  of  moving  the  piston  against  the  external  resistance,  in 
addition  to  raising  the  temperature  of  the  air.  Theory  indi- 
cates, and  experiment  shows,  that  the  excess  of  heat  (KP—KV) 
required  in  the  latter  case  is  equal  to  the  amount  of  work  done 
by  the  air  in  expanding  against  a  constant  pressure. 

The  above  specific  heats  are  for  dry  air.  They  will  be  used 
throughout  this  treatise,  although  the  presence  of  moisture  in  the 
air  slightly  modifies  these  values. 

9.  Absolute  Zero. — Direct  experiment,  in  which  air  at  constant 
pressure  was  exposed  to  various  temperatures,  has  shown  that 
the  volume  which  it  occupies  at  a  temperature  of  32°  Fahr. 
increases  or  decreases  by  1/493  of  this  volume  for  each  increase  or 
decrease  of  1°  Fahr. 

From  this  it  follows  that  air  heated  under  constant  pressure  to  a 
temperature  of  boiling  water  (212°  Fahr.)  has  increased  in 

010 Q9     180 

volume  by— 493— =  493  =  0.366  or  36  per  cent,  of  the  volume 

it  occupied  at  32°  Fahr.  The  same  air  at  493°  below  the  freezing 
point  of  water  or  461°  below  0°  Fahr.  would  have  shrunk 
,  32+461  493  f 

— 493 — ==493       lts  volume>  or  by  that  volume  itself.     The 

temperature  at  which  this  is  assumed  to  take  place  is  called  "the 
absolute  zero."  For  ordinary  compressed  air  problems  it  is  taken 
as  461°  below  0°  Fahr.  This  value  is  used  throughout  this 
treatise. 

10.  Absolute    Temperature. — Absolute    temperature    is    the 
temperature  above  the  absolute  zero.     It  is  usually  designated 
by  T  while  temperatures  in  degrees  Fahr.  are  designated  by  t. 
At  60°  Fahr.  the  absolute  temperature  T  is  60° +461°  =  521°. 
At  0°  Fahr.  the  absolute  temperature  T  is  0°-|-4610  =  4610.     At 
-30°  Fahr.  the  absolute  temperature  is  -30° +461°  =  431°. 


THE  PHYSICAL  PROPERTIES  OF  AIR  5 

11.  Gage  and  Absolute  Pressures. — Ordinary  gages  register 
pressures  above  atmosphere.     Thus,  if  the  air  gage  of  a  com- 
pressor shows  80  Ib.  pressure,  it  indicates  that  the  pressure  of  the 
compressed  air  is  80  Ib.  per  square  inch  above  the  pressure  of  the 
atmosphere.     To  find  the  absolute  pressure  of  air  compressed 
at  sea  level  to  80  Ib.,  we  must  add  14.7  to  the  gage  reading;  thus 
80+14.7  =  94.7  Ib.  absolute.     The  pressures  indicated  by  the 
gage  are   called  gage  pressures;  pressures   above  vacuum   are 
called  absolute  pressures.     To  obtain  absolute  pressure  at  any 
altitude,  add  atmospheric  pressure  at  that  altitude  to  the  gage 
pressure. 

.  From  Table  VI  atmospheric  pressure  at  10,000  ft.  elevation  is 
10.07  Ib.  per  square  inch.  Hence  a  gage  pressure  of  100  Ib.  at  an 
altitude  of  10,000  ft.  is  equal  to  100+10.07  =  110.07  Ib.  absolute 
pressure. 

12.  Free  Air. — Free  air  is  a  term  constantly  used  in  dealing  with 
problems  of  air  compression.     It  is  air  at  normal  atmospheric 
pressure  as  taken  into  the  cylinder  of  a  compressor. 

13.  Isothermal    Compression    or   Expansion   of   Air. — From 
experiment  we  find  that  heat  is  generated  in  the  act  of  compress- 
ing air.     If  during  compression  the  air  could  be  kept  at  constant 
temperature  by  the  abstraction  of  heat  as  fast  as  it  was  generated, 
the  air  would  then  be  said  to  be  compressed  isothermally. 

In  expanding  against  an  external  resistance,  the  air  gives  up, 
or,  to  speak  more  correctly,  converts  heat  into  mechanical 
energy.  If  as  much  heat  could  be  supplied  and  as  fast  as  it  is 
consumed,  the  air  would  be  said  to  expand  isothermally.  In 
isothermal  compression  or  expansion  the  air  remains  at  constant 
temperature  throughout  the  operation. 

14.  Adiabatic  Compression  or  Expansion. — If  during  com- 
pression the  air  neither  loses  nor  gains  heat,  the  heat  generated 
by   the  compression  remaining  in  the  air  and  increasing  its 
temperature,  then  the  air  is  said  to  be  compressed  adiabatically. 
When  the  compressed  air  is  allowed  to  expand  against  an  ex- 
ternal resistance  its  temperature  falls,  and  if  the  air  during  this 
operation  receives  no  heat  from  without,  it  is  said  to  expand 
adiabatically. 


CHAPTER  II 

BEHAVIOR  OF  AIR  UNDERGOING  COMPRESSION  AND  UNDER 
THE  APPLICATION  OF  HEAT 

There  are  two  fundamental  laws  governing  the  behavior  of 
air  undergoing  compression  and  under  the  application  of  heat. 
These  laws  express  the  relations  existing  between  volume, 
pressure  and  temperature. 

15.  Boyle's  or  Mariotte's  Law.  —  The  temperature  remaining 
constant,  the  volume  of  a  given  weight  of  air  varies  inversely  as 
the  absolute  pressure. 


whence  Vi=V- 

r\ 

and  Pl=PVl 

in  which  V  =  volume  of  a  given  weight  of  air  at  an  absolute 

pressure  P. 

•/i  =  volume  of  the  same  weight  of  air  at  the  same 
temperature  and  at  any  absolute  pressure  PI. 

ExampU.  —  One-hundred  cubic  feet  of  free  air,  compressed  isother- 
mally  at  sea  level  to  60  lb.  gage  will  occupy  a  volume: 


Conversely,  19.68  cu.  ft.  of  air  at  60  lb.  gage,  when  expanded  isother- 
mally  down  to  atmospheric  pressure,  will  occupy  a  volume: 


16.  Boyle's  Law  may  also  be  expressed  as  follows:  The  tem- 
perature remaining  constant,  the  product  of  the  pressure  P 
and  the  volume  7  is  a  constant. 


P1V1  =  constant 

6 


AIR  UNDERGOING  COMPRESSION  AND  HEATING  7 

Example.  —  It  has  been  found  that  at  sea  level  1  Ib.  of  air  at  atmos- 
pheric pressure  and  at  32°  Fahr.  occupies  a  volume  of  12.387  cu.  ft. 
If  we  let  P  =  absolute  pressure  in  pounds  per  square  foot 

V  =  volume  of  air  in  cubic  feet 

Then  for  P  =  (14.7X144)  =2116.8  Ib.  per  square  foot 
and          V  =  12.387  cu.  ft, 

PV  =  2116.8X12.387  =  26,220,  nearly. 

If  the  pressure  is  increased  under  constant  temperature  to  two  atmos- 
pheres or  29.4  Ib.  absolute  per  square  inch,  the  volume  of  the  pound  of 
air  will  have  been  reduced  to  one-half  of  the  original  volume.  We  will 
then  have: 

P!  =  (29.4X144)  =4233.6   Ib.  per  square  foot 

Fi  =  12.387X1/2  =  6.1935  cu.  ft. 
whence  PtFi  =  4233.6X6.1935  =  26,220 
and  PV  =  PiFi  =  constant 

17.  Charles'  or  Gay  Lussac's  Law.  —  If  the  pressure  remains 
constant,  every  increase  of  temperature  of  1°  Fahr.  produces  in  a 
given  quantity  of  air  an  expansion  of  1/493  of  the  volume  it 
occupies  at  a  temperature  of  32°  Fahr. 


in  which  Vi  =  volume  of   a  given    weight  of   air   at   t°   Fahr. 

above  the  freezing  point. 
V  =  volume  of  same  weight  of  air  at  freezing  point  (32° 

Fahr.). 
t  =  number   of  degrees  rise   in   temperature    above 

freezing  point. 
a  =  coefficient  of  expansion  =  1/493. 

Example.  —  One  pound  of  atmospheric  air  at  32°  Fahr.  at  sea  level 
occupies  a  volume  V=  12.387  cu.  ft.  At  a  temperature  of  62°  Fahr. 
and  at  the  same  absolute  pressure  it  would  occupy  a  volume: 

F!=  12.387  (1+^X30)  =  13.141  cu.  ft. 

18.  Charles'  Law  may  also  be  expressed  as  follows:     Under 
constant  pressure  the  volume  which  a  given  weight  of  air  occupies 
at  different  temperatures,  varies  directly  as  the  absolute  tem- 
peratures. 
Let     V  =  volume  of  a  given  weight  of  air  at  an  absolute  pressure 

P  and  an  absolute  temperature  T. 

Fi  =  volume  of  the  same  weight  of  air  at  the  same  absolute 
pressure  P  and  at  any  absolute  temperature  T\. 


g  COMPRESSED  AIR 

Then 

VVJFi 

V  ~T 

T 
whence  ^  i  =  V  ^r 

T-TVl 
and  *  *  ~~  •*  y 

Example.—  One  pound  of  air  at  32°  Fahr.  and  at  atmospheric  pres- 
sure at  sea  level  occupies  a  volume  V=  12.387  cu.  ft.  At  a  temperature 
of  62°  Fahr.  and  at  atmospheric  pressure  it  would  occupy  a  volume: 


.13.141  cu.  ft. 


Column  2  of  Table  II  gives  the  volume  in  cubic  feet  occupied  by 
1  Ib.  of  air  at  various  temperatures,  at  sea  level. 

19.  Another  deduction  may  be  made  from  Charles'  Law  as 

follows:     If  a  certain  weight  of  air  be  heated  to  different  tem- 

peratures in  a  closed  cylinder  so  that  its  volume  remains  constant, 

the  absolute  pressures  vary  directly  as  the  absolute  temperatures. 

p  _T^ 

Pi    Tt 

T 
whence  Pi  =P  ^ 

and  Tl=sT^ 

Example.  —  Let  absolute  pressure  of  a  volume  of  free  air  at  a  tempera- 
ture of  62°  Fahr.  be  14.7  Ib.  per  square  inch.  If  heated  to  a  temperature 
of  200°  Fahr.  without  changing  its  volume,  the  absolute  pressure  of 
the  heated  air  would  be: 


px  =  PTT1  =  14.7  X  =  18.58  Ib.  absolute  or  3.88  Ib.  gage. 


20.  Boyle's  and  Charles'  Laws  Combined.  —  Given  a  quantity 
(weight)  of  air  which  has  a  volume  V,  a  pressure  P,  and  a  tem- 
perature T,  we  can  change  it  to  a  condition  in  which  its  volume 
is  Vi,  its  pressure  PI,  and  its  temperature  TV  First:  Change 
the  pressure  from  P  to  PI  under  constant  temperature  T,  then 
find  the  new  volume  Vn  from  Boyle's  Law: 

Vn         P 

=  (1) 


AIR  UNDERGOING  COMPRESSION  AND  HEATING  9 

Second:  Change  the  temperature  of  this  volume  Vn  from  T 
to  TI  under  constant  pressure  PI.  Then  find  the  new  volume 
Vi  from  Charles'  Law: 

Yl-Il  (2) 

V  ~  T 

Multiplying  equations  (1)  and  (2)  we  get: 

VnVi    PTl 
VnV~P1T 

Whence  PiFi=PFy  (3) 

In  Article  16  it  was  shown  that  for  1  Ib.  of  air  at  32°  Fahr. 
and  at  atmospheric  pressure: 

PV  =  26,220 
Substituting  this  value  in  equation  (3)  we  get: 


PlVl  =32+46l  Tl  =53'2  Tl  nearly  (4) 

The  equation  is  usually  written: 

PV  =  RTorP1V1  =  RTl  (5) 

in  which 

P  and  PI  =  absolute  pressures  in  pounds  per  square  foot 

V  =  volume  in  cubic  feet  which  1  Ib.  of  air  occupies  at 
a  temperature  of  32°  Fahr.  and  at  atmospheric 
pressure  (14.7  Ib.) 

Vi=  volume  in  cubic  feet  which  1   Ib.  of  air  occupies 
at  an  absolute  pressure  Pi  and  an  absolute  tem- 
perature TI 
R  =  constant  =  53.2. 

From  equation  (5)  we  deduce: 


if  this  volume  of  air  be  raised  1°  in  temperature  at  constant 
pressure,  its  volume  will  become: 


10  COMPRESSED  AIR 

The  change  of  volume  will  be: 


whence  Pi(Fa-70  =JR(7T1+1-T1)  =  #  (6) 

The  first  term  of  the  equation  is  the  work  done  by  the  pound 
of  air  in  expanding  against  a  constant  pressure  PI  while  the 
temperature  of  the  air  is  rising  1  degree.  In  Article  8  it  was 
stated  that  this  work  is  equal  to  the  difference  in  the  specific 
heats,  expressed  in  foot-pounds. 
Hence  we  may  write: 

R  =  (KP-KV)  =  184.8  -13  1.6  =53.2  (7) 

which  is  the  same  as  the  value  deduced  in  equation  (4). 

Example.—  One  pound  of  air  at  32°  Fahr.  (!T  =  461+32)  and  at  atmos- 
pheric pressure  P  (14.7)  occupies  a  volume  7=12.387  cu.  ft. 

If  we  compress  this  pound  of  air  under  constant  temperature  T  to 
100  Ib.  gage  (Pi  =  114.7  Ib.)  we  find  the  new  volume  Vn  from  equation  (1). 

V*  =  12.387-^  =  1.588  cu.  ft. 

If  we  heat  this  volume  Vn  of  air,  which  still  weighs  1  Ib.,  from  32°  Fahr. 
to  150°  Fahr.  (7*!  =  461  +  150)  under  constant  pressure,  we  find  the  new 
volume  FI  from  equation  (2): 

=1.967  cu.  ft. 


Expressing  P!  in  pounds  per  square  foot=  144X114.  7  =  16,517  Ib. 
We  get  Pi  F!  =  16,517  XI.  97  =  32,500 

The  same  result  could  have  been  obtained  directly  from  equation  (4) 
PiF!  =  53.2  T1 

P!F!  =  53.2  (150+461)  =32,500 

In  employing  formulas  (4)  and  (5)  of  this  article,  it  must  be  borne 
in  mind  that  the  pressures  are  expressed  in  pounds  per  square  foot,  and 
that  the  quantity  of  air  contained  in  the  volume  is  1  Ib. 

WEIGHT  OF  AIR 

21.  Weight  of  Equal  Volumes  of  Air  at  Constant  Pressure 
and  Varying  Temperatures.—  Let  a  cylinder  (Fig.  1  a)  with  a 
movable  piston,  be  filled  with  a  given  weight  of  air  at  an  absolute 
temperature  T  and  an  absolute  pressure  P  in  pounds  per  square 
inch,  occupying  a  volume  Va. 


WEIGHT  OF  AIR 


11 


If  heat  is  applied  to  the  cylinder  (a)  the  air  in  it  will  expand 
under  constant  pressure  and  the  piston  will  assume  the  position 
shown  in  Fig.  1  6.  The  weight  of  this  air  has  remained  the  same 
and  so  has  the  pressure,  but  the  volume  and  the  absolute  tempera- 
ture have  increased,  while  the  density  of  the  mass  of  air  has 
decreased. 

If  we  now  cut  off  from  Fig.  1  6  a  volume  equal  to  the  volume 
Va  in  Fig.  1  a  it  is  evident  that  the  weight  W i  of  the  volume  Va 
in  cylinder  (6)  is  less  than  the  weight  of  volume  Va  in  cylinder  (a). 


VOLUME  =  Va 
ABSOL.  PRESS  .=  P 
ABSOL.  TEMP.=T 
WEIGHT  =  W 


VOLUME  =  Va 
ABSOL.  PRES8.=  P 
ABSOL.  TEMP.  =Tl 

WEIGHT  =  VV 
FIG.  1. 


VOLUME        =     V& 
ABSOL.  PR£33?R 

BSOl.  TEMP.=Tl 
-VE.GHT        =     W 


This  shows  that  of  two  equal  volumes  of  air  having  the  same 
absolute  pressure,  the  one  having  the  higher  temperature  has 
the  less  weight.  The  exact  relation  may  be  derived  from  the 
equations  in  Article  18.  It  is  stated  as  follows: 

The  weight  of  two  equal  volumes  of  air,  having  the  same 
absolute  pressure,  varies  inversely  as  the  absolute  temperatures. 

W  _Ti 
Wi~~  T 

in  which  W  =  weight  of  a  given  volume  of  air  at  an  absolute 

temperature  T 

Wi  =  weight  of  an  equal  volume  of  air  at  an  absolute 
temperature  TI 

22.  Weight  of  Equal  Volumes  of  Air  at  Constant  Temperature 
and  Varying  Pressures. — Let  a  cylinder  (Fig.  2  6)  having  a 
movable  piston  be  filled  with  a  given  weight  of  air  occupying  a 
volume  Vb  and  having  an  absolute  pressure  P  and  an  absolute 
temperature  T. 

If  we  load  the  piston  with  an  additional  weight  (w),  the 
piston  will  descend  in  the  cylinder  to  the  position  shown  in 
Fig.  2  a.  The  weight  of  the  air  in  cylinder  (a)  has  remained 


12 


COMPRESSED  AIR 


the  same,  and  the  absolute  temperature  is  assumed  to  have  also 
remained  the  same.  But  the  abso  ute  pressure  has  increased 
and  with  it  the  density  of  the  air. 

If  we  now  cut  off  from  the  cylinder  (6)  a  volume  Va  equal  to 
the  volume  in  cylinder  (a),  it  is  evident  that  the  weight  of  volume 
Va  in  cylinder  (6)  is  less  than  the  weight  of  volume  Va  in  cylinder 
(a) .  This  shows  that  of  two  equal  volumes  of  air  having  the  same 
absolute  temperature,  the  one  having  the  less  pressure  has  the  less 
weight,  and  vice  versa.  The  exact  relation  may  be  derived  from 
the  equations  in  Article  15.  It  is  stated  as  follows: 


FIG.  2. 

The  weight  of  two  equal  volumes  of  air,  having  the  same 
absolute  temperature,  varies  directly  as  the  absolute  pressures. 
W  _P 
Wl~Pl 

in  which  W  =  weight  of  a  given  volume  of  air  at  an  absolute 

pressure  P 

Wi  =  weight  of  an  equal  volume  of  air  at  an  absolute 
pressure  PI 

23.  Weight  of  1  cu.  ft.  of  Air  at  Atmospheric  Pressure  P  at 
Sea  Level  and  at  any  Absolute  Temperature  TV— According  to 
Article  2,  1  cu.  ft.  of  air  at  atmospheric  pressure  at  sea  level  and 
'  Fahr.  weighs  0.0764  lb.;  hence  the  weight  W1  of  1  cu.  ft. 
of  air  at  atmospheric  pressure  but  at  an  absolute  tempera- 
ture Tl  is 


~    whence 


(60+461)     39.804 


Thus,  we  find  the  weight  of  1  cu.  ft.  of  air  at  atmospheric  pres- 
mre  at  sea  level  and  at  any  absolute  temperature  T,  by  dividing 
the  constant  39.804  by  the  absolute  temperature  7\ 


WEIGHT  OF  AIR  13 

24.  Weight  of  1  cu.  ft.  of  Air  at  any  Absolute  Temperature  Tt 

39  804 
and  any  Absolute  Pressure  PL—  We  have  as  before  :  TFi  =  —  ^  — 

li 

=  weight  of  1  cu.  ft.  of  air  at  atmospheric  pressure  at  sea  level 
and  at  any  absolute  temperature  TV 

If  we  now  designate  by  Wz  the  weight  of  1  cu.  ft.  of  air  at  the 
same  absolute  temperature  T\  but  at  any  absolute  pressure  P\ 
we  have  from  Art  22: 

Wi     atmospheric  pressure  at  sea  level 
~ 


W,~  Pl 

39  804      14  7 

Substituting  the  value  of  W\  from  Art.  23  we  get     m  Tr/  =   p 

liWz       f\ 

whence  W2  =  2.7077  -jr  (1) 

Thus,  we  find  the  weight  of  1  cu.  ft.  of  air  at  any  absolute  pres- 
sure and  temperature  by  multiplying  the  absolute  pressure  in 
pounds  per  square  inch  by  the  constant  2.7077  and  dividing  the 
product  by  the  absolute  temperature. 

Example.  —  The  weight  of  1  cu.  ft.  of  air  at  60  Ib.  gage  and  at  100° 
Fahr.  at  sea  level  is: 


=0.3602  Ib. 


Table  I  gives  the  weight  of  1  cu.  ft.  of  air  at  various  gage  pressures  and 
temperatures  at  sea  level. 

24a.  When  using  formula  (1),  Article  24  for  computing  the 
weight  of  1  cu.  ft.  of  air  at  an  elevation  above  sea  level,  it  must 
be  borne  in  mind  that  PI  in  that  case  is  the  gage  pressure  plus 
the  atmospheric  pressure  at  that  elevation. 

Example.  —  What  is  the  weight  of  1  cu.  ft.  of  air  at  60  Ib.  gage  and  at 
100°  Fahr.,  at  an  elevation  of  8000  ft.  above  sea  level? 

From  Table  VI,  atmospheric  pressure  at  an  altitude  of  8000  ft.  above 
sea  level  is:  10.87  Ib.  per  square  inch;  hence: 

Ib. 


CHAPTER  III 
THE  COMPRESSION  OF  AIR  IN  AIR  COMPRESSORS 

25.  The  Air  Cylinder  of  a  Compressor. — Fig.  3  shows  the  air 
cylinder  (A)  of  a  reciprocating  compressor,  in  which  the  air  is 
compressed  by  a  piston  (B),  whose  rod  (C)  is  connected  to  the 
piston  of  a  steam  engine  or  through  a  connecting  rod  and  crank  to 
a  revolving  shaft,  the  latter  being  driven  by  some  form  of  prime 
mover. 

The  cylinder  shown  is  that  of  a  single-stage  compressor,  in 
which  the  air  is  compressed  in  one  operation  and  in  one  cylinder, 
from  initial  to  final  pressure.  In  two-  and  multi-stage  compress- 
ors the  air  is  compressed  gradually  in  succeeding  cylinders, 
being  cooled  to  in-take  temperature  while  passing  from  one 
cylinder  to  the  next  one.  (See  Article  57.) 

26.  Water-jackets. — As  shown  in  Fig.  3,  the  cylinder  heads 
and  usually  the  main  body  of  the  air  cylinders  are  water-jacketed. 
The  chief  object  of  this  is  to  prevent  the  cylinders  from  reaching 
a  temperature  which  would  vaporize  the  lubricating  oil  and  thus 
cause  rapid  wear  of  piston  and  cylinder.    Incidentally  the  air  itself 
is  cooled  to  some  extent  by  the  surrounding  water,  which  means 
a  gain  in  efficiency. 

27.  Inlet  and  Discharge  Valves. — Modern  compressors  as  a 
rule  are  double  acting,  that  is,  air  is  taken  in,  compressed,  and 
discharged  on  the  forward  stroke  as  well  as  on  the  backward 
stroke  of  the  piston.     For  this  reason  each  of  the  cylinder  heads 
carries  one  or  more  inlet  valves  a,  a'  through  which  the  atmos- 
pheric  air  can  enter  the  cylinder,   and  one  or  more  discharge 
valves  b,   b'  which  open  outward  into  closed  ports  g,  h   con- 
nected by  a  conduit  c,  which  leads  to  a  closed  receiver  R,  whence 
the  compressed  air  is  conveyed  to  the  place  where  it  is  proposed 
to  use  it.     The  inlet  and  discharge  valves  are  either  mechanically 
moved,  resembling  in  their  general  form  and  operation  the  steam 
valves  of  a  Corliss  engine,  or  they  are  of  the  poppet  type,  being 
pressed  upon  their  seats  by  a  spring.     In  Fig.  3,  which  shows  the 
section  of  the  air  cylinder  of  an  air  compressor,  the  inlet  valves 

14 


COMPRESSION  OF  AIR  IN  AIR  COMPRESSORS  15 

a,  a'  are  mechanically  moved,  the  discharge  valves  6,  V  are  of  the 
poppet  type.     For  description  of  valves  see  Articles  144-153. 

28.  Analysis  of  Single-stage  Compression.— At  the  beginning 
of  the  stroke  all  valves  are  closed.  The  piston  moving  from  right 
to  left,  as  shown  in  the  figure,  causes  a  partial  vacuum  behind  it; 


SAFETY  VALVE 


-PRESSURE  GAUGE 


FIG.  3. — Diagram  Illustrating  Principle  of  Single-stage  Compression 

the  inlet  valves  open  under  atmospheric  pressure  (unless  opened 
mechanically)  and  the  outside  ofr  free  air  rushes  into  the  cylinder 
behind  the  receding  piston. 

On  the  left-hand  side  of  the  piston  we  have  at  the  beginning  of 
the  stroke  a  cylinder  full  of  atmospheric  or  free  air,  which  by 
the  advancing  piston  is  compressed  into  a  steadily  decreasing 
volume.  The  pressure  of  the  air  on  this  side  of  the  piston  is  at 


16  COMPRESSED  AIR 

the  same  time  steadily  increasing  until  at  a  certain  point  of  the 
stroke  it  reaches,  or  slightly  surpasses,  the  receiver  pressure. 
Beyond  this  point  the  increasing  pressure  causes  the  discharge 
valves  to  open,  and  to  the  end  of  the  stroke  the  compressed  air  is 
delivered  into  the  receiver  under  constant  pressure. 

If  the  inlet  valves  in  the  left-hand  side  of  the  cylinder  are  of  the 
poppet  type,  they  are  kept  closed  during  the  forward  stroke  of  the 
piston  by  the  pressure  of  the  air  inside  the  cylinder,  which  is 
greater  than  the  outside  atmospheric  pressure. 

29.  The  Receiver  pressure  depends  on  the  work  which  the 
compressed  air  is  to  perform.  If,  for  instance,  the  air  engines 
at  the  end  of  the  pipe  line  require  a  pressure  of  80  Ib.  gage,  no 
air  is  to  be  drawn  from  the  pipe  line  until  the  gage  of  the  receiver 
near  the  compressor  shows  this  pressure,  plus  the  pressure 
required  for  transmission.  After  this,  the  supply  of  compressed 
air  must  keep  pace  with  the  demand.  Should  the  demand  exceed 
the  supply,  the  pressure  of  the  air  would  drop  below  80  Ib.,  thereby 
impairing  the  efficiency  of  the  air  engines.  If  on  the  other  hand 
the  supply  at  any  time  should  exceed  the  demand,  the  pressure 
of  the  air  in  the  receiver  and  in  the  pipe  line  would  increase  until  it 
reaches  the  pressure  for  which  the  safety-valve  of  the  receiver  is 
set,  when  it  will  blow  off  through  the  latter. 

As  this  means  a  waste  of  energy,  compressors  which  furnish 
air  for  intermittent  work  are  generally  supplied  with  automatic 
regulating  devices,  such  as  are  described  and  illustrated  in 
Articles  157-160. 


CHAPTER  IV 

THEORY  OF  AIR  COMPRESSION 
A.  ISOTHERMAL  COMPRESSION 

30.  According  to  Boyle's  Law,  at  constant  temperature  the 
volume  occupied  by  a  given  weight  of  air  varies  inversely  as  the 
absolute  pressure: 


v 

whence  Pi  =PTT 

in  which  V  =  the  volume  of  a  given  weight  of  air  at  an  absolute 

pressure  P  and  a  certain  temperature. 
V\  =  the  volume  of  the  same  weight  of  air  at  the  same 
temperature  and  at  any  absolute  pressure  PI. 

Take,  for  instance,  1  cu.  ft.  of  free  air  at  60°  Fahr.,  having 
an  absolute  pressure  of  one  atmosphere  or  14.7  Ib.  per  square 
inch.  Assume  that  this  air  is  confined  under  the  piston  of  a 
closed  cylinder,  and  that  driving  the  piston  forward  we  reduce 
the  volume  occupied  by  the  air  to  1/2  cu.  ft.,  at  the  same  time 
maintaining  its  temperature  at  60°  Fahr.,  then  the  absolute 

pressure  of  the  air  would  be  PI  =  14.7  Xjv  =  29.4  Ib.per  square 

inch,  or  twice  what  it  was  before. 

If  the  volume  were  reduced  to  1/3  cu.  ft.,  its  absolute  pressure 
would  become  3X14.7  =  44.1  Ib.  per  square  inch,  or  29.4  Ib. 
gage,  always  upon  the  condition  that  the  temperature  remains  at 
60°  Fahr. 

In  other  words,  if  the  volume  of  air  becomes  1/2,  1/3,  1/4,  etc., 
times  the  original  volume,  its  pressure  becomes  2,  3,  4,  etc., 
times  the  original  pressure,  always  taking  absolute  pressures. 

31.  Graphical  Illustrations  of  Isothermal  Compression.  —  Let 
Fig.  4  represent  the  air  cylinder  of  a  compressor,  48  in.  long 
with  a  piston  moving  in  it  in  the  direction  of  the  arrow.  Let 
2  17 


18 


COMPRESSED  AIR 


the  cylinder  be  connected  to  a  receiver  in  which  the  pressure 
is  73.5  Ib.  gage  or  six  atmospheres  per  square  inch. 

Assume  that  the  cylinder  has  been  filled  with  atmospheric 
air  during  the  suction  stroke  of  the  piston.  By  moving  the 
piston  12  in.  from  the  left  to  the  right,  the  volume  of  the  air 

AC)        -i  rt        o 

is  reduced  to  — j~ — =T  of  the  original  volume  and  the  pressure 

has  increased  to  4/3  times  the  atmospheric  pressure,  that  is,  to 
4/3X14.7=19.6  Ib.  absolute  or  4.9  Ib.  gage. 


-TOTAL  ORIGINAL  VOLUME" 


FIG.  4.— Diagram  Illustrating  Isothermal  Compression  and  Delivery. 


When  the  piston  has  advanced  to  a  point  24  in.  from  its  first 

position,  the  volume  of  air  has  been  compressed  to  —  ~, —  =  ~ 

48          2 

of  the  original  volume  and  the  pressure  is  now  twice  that  of  the 
atmosphere,  that  is;  29.4  Ib.  absolute  or  14.7  Ib.  gage. 

The  same  reasoning  applies  to  other  positions  of  the  piston 
until  the  latter  reaches  a  point  40  in.  from  the  starting  point. 
The  air  has  now  been  reduced  to  ^^ =\  of  the  original  volume 
and  the  pressure  has  increased  to  six  atmospheres,  that  is,  88.2 


THEORY  OF  AIR  COMPRESSION  19 

lb.  absolute  or  73.5  Ib.  gage.  This  being  the  pressure  in  the 
receiver,  the  discharge  valves  open  and  the  remaining  8  in.  of 
the  stroke  are  completed  by  the  piston  against  a  constant  pressure 
of  73.5  lb.  in  delivering  the  air  into  the  receiver. 

32.  Construction  of  the  Isothermal  Compression  Curve. — Draw 
a  horizontal  line,  AD,  which  at  a  convenient  scale  represents 
48  in.  and  mark  on  this  line  points  at  12,  24,  and  40  in.  from  its 
left  end;  then  draw  at  those  points  lines  perpendicular  to  AD. 

On  these  lines,  measure  off,  at  any  other  convenient  scale, 
the  gage  pressures  corresponding  to  the  stroke;  this  will  give  a 
succession  of  points  a,  b,  c,  d,  and,  if  we  join  them  by  a  continuous 
line,  we  get  a  curve  A-B  which  represents  the  variations  of  air 
pressure  during  the  compression;  that  is,  the  gage  pressure  at 
any  point  M  is  measured  by  the  line  MN. 

The  curve  AB  is  a  hyperbola  and  is  known  as  the  curve  of 
isothermal  compression.  Its  equation  is : 

PV  =  constant 

If  we  took  any  number  of  intermediate  points  between  40  and 
48  in.  of  the  stroke,  the  pressure  would  always  be  73.5  lb.  gage, 
consequently  a  line  drawn  connecting  these  points  will  be  a 
straight  line  parallel  to  AD.  It  represents  the  period  of  delivery 
under  constant  pressure. 

33.  Work    of    Isothermal,    Single-stage    Compression    and 
Delivery. — Work  is  the  product  of  a  force  and  the    distance 
through  which  it  acts  in  the  direction  of  its  application. 

In  the  diagram,  Fig.  5,  let  AB  represent  an  isothermal  com- 
pression curve 

BC  =  the  line  of  delivery 
PI  and  P2  =  absolute  initial  and  terminal  pressures  in  pounds 

per  square  inch 
L  =  length  of  stroke  in  feet. 

The  force  acting  on  the  body  of  air  contained  in  the  cylinder 
is  the  force  applied  to  the  piston  by  some  external  agent,  such  as 
steam,  water,  electricity,  etc.  The  displacement  of  the  point 
of  application  during  one  stroke  of  the  piston  is  the  length  of  the 
stroke  (L). 

The  force  applied  to  the  piston  must  be  equal  (theoretically) 
to  the  resistance  offered  by  the  air  inside  the  cylinder,  that  is,  to 


20 


COMPRESSED  AIR 


its  pressure,  which  at  any  point  of  the  stroke  is  proportional  to 
the  volume  into  which  the  air  has  been  compressed. 

During  compression  of  the  air  from  A  to  B  the  pressure  in- 
creases from  an  absolute  pressure  PI  to  an  absolute  pressure  P2; 
during  the  remainder  of  the  stroke  from  B  to  C  the  air  which  now 
occupies  a  volume  F2,  represented  by  the  distance  BC,  is  de- 
livered into  the  receiver  at  a  constant  absolute  pressure  P2. 


^3 
^  AIR    CYLINDER 

U LENGTH   OF   STROKE  =  L   FEET      —          J 

i P 


FIG.  5. 

The  average  resistance  of  the  air  during  the  entire  stroke  is  the 
mean  pressure  of  the  air  against  the  piston.  Its  value  in  terms  of 
absolute  pressure  in  pounds  per  square  inch  is  represented  by  a 
line  EF,  located  somewhere  between  M  and  0. 

Let    A  =  area  of  piston  in  square  feet 
L  =  length  of  stroke  in  feet 
PI  =  absolute  initial  pressure  of  in-take  air  in  pounds  per 

square  inch 

PI  =  absolute  terminal  pressure  in  pounds  per  square  inch 
Pe  =  mean  absolute  pressure  in  pounds  per  square  inch 
W  =  total  work  performed  per  stroke  in  foot-pounds 
Tfn  =  net  work  performed  per  stroke  in  foot-pounds 
Vi  =  volume  of  free  air  in  cubic  feet  taken  into  the  cylinder 

per  stroke 
F2  =  volume  of  air  in  cubic  feet  after  being  compressed  to  an 

absolute  pressure  P2. 


THEORY  OF  AIR  COMPRESSION  21 

The  total  mean  force  acting  on  the  piston  during  the  entire 
stroke  is  144  PeA  Ib.  and  the  total  work  performed  per  stroke  is 

TP  =  144P€ALft.-lb. 
But  AL  =  V! 

hence  TF  =  144P.V1  ft.-lb.  (1) 

If  in  the  diagram,  Fig  5,  we  substitute  for  the  length  of  the  stroke 
(L)  the  volume  Vi  in  cubic  feet  of  free  air,  taken  into  the  cylinder 
per  stroke,  then  the  product  PeVi  in  equation  (1)  is  equal  to  the 
numerical  value  of  the  area  MA  SCO.  This  value  is  obtained 
by  multiplying  Pe,  expressed  in  pounds  per  square  inch,  with  V\, 
expressed  in  cubic  feet. 

The  total  work  done  during  one  stroke  of  the  piston  is  as  follows: 

Wi  =  work  of  compressing  a  volume  V\  of  free  air  from  an 
absolute  pressure  PI  to  an  absolute  pressure  P-i.  This 
work  is  proportional  to  the  area  MABR. 

w3  =  work  of  delivering  the  compressed  air  which  now  occu- 
pies a  volume  Vz  into  the  receiver  under  a  constant 
absolute  pressure  Pa.  This  work  is  proportional  to  the 
area  BCOR. 

The  sum  of  the  two  quantities  Wi  and  w2  includes 

W3  =  work  of  filling  the  cylinder  behind  the  advancing 
piston  with  a  new  volume  of  free  air  which  is  to  be 
compressed  during  the  return  stroke  of  the  piston. 
This  work  is  proportional  to  the  area  MADO. 

The  work  ws,  however,  is  not  performed  by  energy  supplied 
by  the  compressor,  but  by  the  pressure  of  the  in-take  (atmos- 
pheric) air.  Measured  in  foot-pounds  it  is 


in  which  the  product  P\V\  is  equal  to  the  numerical  value  of 
the  area  MADO. 

34.  The  net  work  Wn  in  foot-pounds  performed  by  the  com- 
pressor during  one  stroke  of  the  piston  is,  therefore: 

W  n  =  144  X  (area  MABCO  minus  area  MADO) 
=  144  X  (shaded  area  ABCD} 


22  COMPRESSED  AIR 


But  area  ABCD  =  are&  MABR 
plus    area  BCOR 
minus    area  A  DOM 


•I, 


For  isothermal  compression  PF=PiFi 


PdF 

nVi 


Hence  Area  MABR=Pi 

=PiFi  Naperian  log  yl 

and  since  y  =P 

Area  MABR  =  PiVi  Naperian  log  p-. 
Area    BCOR=PZV2 


Therefore,    TFn  =  144  (P^i  Naperian  log  j 

and  since  under  isothermal  conditions  P2F2  =  PiFi. 

35.  Net  Work  of  Isothermal  Compression  and  Delivery  per 
Stroke : 

TFn  =  144P1F1loge^ft.-lb. 

in  which  PI  =  initial  absolute  pressure  in  pounds  per  square 

inch. 

P2  =  final  absolute  pressure  in  pounds  per  square  inch. 
FI  =  volume  of  free  air  in  cubic  feet  taken  into  the 

cylinder  per  stroke. 
loge  =  Naperian  log  =  2.302585  times  common  log. 

36.  Mean    Gage — Pressure,   Isothermal    Compression    and 
Delivery : 

Let    Pm  =  mean  gage  pressure  in  pounds  per  square  inch. 
A  =  area  of  piston  in  square  feet. 
L  =  length  of  stroke  in  feet. 


THEORY  OF  AIR  COMPRESSION  23 

FI  =  volume  of  air  in  cubic  feet  taken  into  the  cylinder  per 

stroke. 
-  Wn  =  net  work  per  stroke  in  foot-pounds. 

Then  W  „  =  144  PmAL  and  since  AL  =  FI 
Wn  =  144  PmF!  whence  Pm=  ^^~ 

T) 


or       Pm  = 


PI  loge  D-  Ib.  per  square  inch. 
r\ 


Column  6  of  Table  III  gives  mean  gage  pressures  for  isothermal 
compression  and  delivery  and  for  various  terminal  gage  pressures. 

37.  Theoretical  Horse-power,  Isothermal  Single-stage  Com- 
pression and  Delivery.  —  The  theoretical  horse-power  required  to 
compress  isothermally  in  one  stage  a  volume  FI  of  free  air  per 
minute  from  an  absolute  pressure  PI  to  an  absolute  pressure  P2 
and  deliver  the  compressed  air  into  the  receiver  under  constant 
pressure  is  found  from  the  general  formula: 

PLAN 
Horse-power  =  33^5 

in  which  P  =  mean  gage  pressure  in  pounds  per  square  inch. 
L  =  length  of  stroke  in  feet. 
A  =  area  of  piston  in  square  inches. 
N  =  number  of  strokes  per  minute. 

If  we  now  let  V\  designate  the  volume  of  free  air  in  cubic  feet 
taken  into  the  cylinder  per  minute,  we  have: 


from  which  LAN  =  U4  V1 

Substituting  this  value  and  the  value  Pm  for  P  in  our  formula, 
we  get 

144  Prfi  .       P2 
Horse-power  =  -33^    log«  Pl 


in  which  V\  =  volume  of  free  air  in  cubic  feet  taken  into  the 

cylinder  per  minute. 

Pi  =  initial  absolute  pressure  in  pounds  per  square  inch. 
P2  =  terminal  absolute  pressure  in  pounds  per  square 

inch. 
loge  =  Naperian  log  =  2.302585  times  common  log. 


24  COMPRESSED  AIR 

Column  3  of  Table  V  gives  the  theoretical  horse-power  required 
to  compress  1  cu.  ft.  of  free  air  per  minute  isothermally  in  one 
stage  to  various  gage  pressures  and  deliver  it  at  that  pressure 
into  the  receiver. 

38.  Isothermal  compression  in  actual  practice  is  impossible  of 
attainment.     It  is  only  approached  in  slow-speed  compressors, 
where  the  air  is  in  contact  with  the  water-jackets  for  a  longer 
time  than  in  normal  speed  machines. 

In  actual  practice  the  compression  curve  as  obtained  from 
indicator  diagrams  falls  closer  to  the  adiabatic  than  to  the 
isothermal  curve.  For  this  reason  the  formulas  for  adiabatic 
compression  are  generally  used  in  practical  compressor  com- 
putations. 

39.  Isothermal  Expansion. — If  compressed  air  could  be  ex- 
panded isothermally  down  to  atmospheric  pressure  in  an  air 
engine,  the  theoretical  work  performed  would  be  the  same  as 
the  work  required  for  isothermal   compression   and   delivery. 
Hence,  work  of  isothermal  expansion : 

Horse-power  =  ^^  log,  g  (1) 

in  which  PI  =  absolute  pressure  of  exhaust  air  in  pounds  per 

square  inch. 

=  atmospheric  pressure. 

Vi  =  volume  in  cubic  feet  per  minute,  which  the  volume 

F2  of  compressed  air,  admitted  into  the  air  engine 

per  minute,   would  occupy  after  expansion  to 

initial  pressure. 

P2  =  absolute  pressure  in  pounds  per  square  inch  of 

the  air  admitted  into  the  air  engine, 
loge  =  Naperian  log  =  2.302585  times  common  log. 
In  expansion  work  we  usually  know  the  volume  F2  of  com- 
pressed air  taken  into  the  cylinder  of  an  air  engine  per  unit  of 
time,  and  since  under  isothermal  conditions 

PitTi=P272 
We  can  also  write: 
Theoretical  horse-power  isothermal  expansion: 


THEORY  OF  AIR  COMPRESSION  25 

in  which  P2  =  absolute  pressure  of  air  taken  into  cylinder  in 

pounds  per  square  inch. 
PI  =  exhaust  (atmospheric)  pressure. 
F2  =  volume  of  compressed  air  in  cubic  feet  taken  into 
the  cylinder  per  minute. 

At  the  present  stage  of  the  art,  isothermal  expansion  is  im- 
possible of  attainment  in  actual  practice.  The  formulas  in- 
troduced under  this  article,  however,  are  useful  for  comparison 
and  for  estimating  efficiencies  of  compressores,  pipe  lines  and  air 
engines. 

B.  ADIABATIC  COMPRESSION  OF  AIR 
THEORY 

40.  We  have  seen  that  if  air  is  compressed,  heat  is  gene- 
rated. 

In  adiabatic  compression  this  heat  is  allowed  to  accumulate 
unchecked  during  the  period  of  compression.  As  a  consequence, 
when  a  certain  pressure  is  reached,  the  corresponding  volume  of 
air  will  be  greater  on  account  of  this  heat  than  the  volume  which 
the  air  would  occupy  if  the  compression  up  to  that  same  pressure 
had  been  isothermal.  When  the  volume  is  reduced  to  one-half, 
the  pressure  is  not  only  double  as  in  isothermal  compression,  but 
more  than  double  because  of  the  heat,  generated  during  compres- 
sion, being  still  in  the  air. 

Again,  when  the  pressure  has  been  doubled,  the  volume  will 
not  be  one-half,  but  will  be  more  than  one-half,  owing  to  the 
expansion  due  to  heat  which  has  remained  in  the  air. 

Since  the  pressure  rises  faster  than  the  volume  diminishes, 

P  Vi 

^-  is  no  longer  equal  to  but  is  greater  than  -T7-     To  form  an 

L\ 

equation,  the  value  of  -^  must  be  increased.     This  is  done  by 

introducing  an  exponent  l'n"  which  raises  the  value  of  ^  to  a 

power  whose  index  has  been  found  to  be  the  ratio  between  the 
specific  heat  of  air  at  constant  pressure,  and  the  specific  heat 
at  constant  volume,  expressed  either  in  heat  units  (B.T.U.'s)  or 
in  foot-pounds. 

_  CP_0,2375  _Kp_184._8 
n  ~  C,~0.1689  -JT.-131. 6~1>41J 


26  COMPRESSED  AIR 

This  gives  for  the  general  equation  of  the  adiabatic  compression 
or  expansion  curve: 

PVn=P1V1n  (2) 

and,  since  the  exponent  n  takes  care  of  the  changes  in  tempera- 
ture, due  to  adiabatic  compression  or  expansion,  we  have  from 
analogy  with  deductions  made  under  Article  16: 

PVn=P1Vln  =  constant  (3) 

jr 

The  synthetical  method  by  which  "n"  is  found  to  equal  ~^- 

Kv 

is  shown  in  Article  117 'a. 

The  value  of  n  varies  slightly  with  the  variation  in  the  specific 
heats  of  air,  due  to  the  presence  of  moisture,  as  pointed  out  under 
Article  8.  Throughout  this  treatise,  the  value 

n  =  1.406 
will  be  used. 


RELATION  BETWEEN  TEMPERATURE,  VOLUME  AND 

PRESSURE  IN  ADIABATIC  SINGLE  STAGE  COM- 

PRESSION OR  EXPANSION  OF  AIR 

41.  The  relation  between  temperature,  pressure,  and  volume 
of  air  at  the  beginning  and  at  the  end  of  adiabatic  single  stage 
compression  or  expansion  can  be  deduced  from  Charles'  and 
Boyle's  Laws  as  follows:  according  to  these  laws  (see  Article  20, 
equation  (3)). 


PiF!=PF  (1) 

£  =  ^  (2) 

For  adiabatic  compression 


combining  equations  (2)  and  (4) 


THEORY  OF  AIR  COMPRESSION  27 

whence  \yj       =  ~  (5) 

anc^  W =  (~TV  H 

Fi      /7V-^  (6) 


from  equation  (3) 


(7) 


V 
or  y 


_/PA 
x"\P/ 


tr,1         /Pl\    n 

whence  If^J       =\p7 


n-l 


=    -— 


combining  with  equation  (5)  ^  =  (-— 


_ 
and  (Y)       =y  (9) 

This  gives  the  following  relations  between  volume,  pressure,  and 
temperature  in  adiabatic  single  stage  compression  or  expansion: 
From  (5)  absolute  temperature  in  terms  of  volumes 


J  (10) 

From  (8)  absolute  temperature  in  terms  of  absolute  pressures 

From  (6)  volume  in  terms  of  absolute  temperatures 

Vi  =  v(-)*^  (12) 

~V/ 


28  COMPRESSED  AIR 

From  (7)  volume  in  terms  of  absolute  pressures 

\-  (13) 


From  (9)  absolute  pressure  in  terms  of  absolute  temperatures 

.      p^pftf'  (14) 

From  (4)  absolute  pressure  in  terms  of  volumes 

in  which    V  =  volume  corresponding  to  an  absolute  pressure  P 

and  an  absolute  temperature  T. 

Vl  =  volume  corresponding  to  an  absolute  pressure 

Pi  and  an  absolute  temperature  Ti  and  vice  versa. 

n  =  exponent  of    adiabatic    compression    (=1.406). 

41a.  Law  of  Thermodynamics,  Applied  to  Adiabatic  Com- 
pression and  Expansion  of  Air. — According  to  the  law  quoted 
under  Article  6  heat  and  work  are  mutually  convertible.  In 
adiabatic  compression  of  air  all  the  work  of  compression  is 
converted  into  heat  (see  Article  117),  and  the  temperature  of  the 
air  is  increased  correspondingly. 

In  compliance  with  the  law  referred  to,  a  volume  of  com- 
pressed and  therefore  heated  air,  if  allowed  to  expand  adiabat- 
ically  to  initial  pressure,  against  an  external  resistance,  would 
perform  work  by  converting  back  into  mechanical  energy  all  the 
heat  received  during  compression.  Theoretically,  the  amount  of 
work  performed  will  be  equal  to  the  work  of  compression.  The 
temperature  of  the  expanded  air  will  be  the  same  as  before 
compression. 

In  compressed-air  installations,  practically  all  of  the  com- 
pression heat  is  abstracted  from  the  air  by  water-cooling  and 
radiation,  previous  to  expansion.  In  this  case  the  compressed 
air  is  still  capable  of  doing  expansive  work  as  before,  by  con- 
verting heat  into  mechanical  energy.  But  the  capacity  for  doing 
work  will  be  less  than  in  the  first  case,  due  to  the  loss  of  the 
compression  heat  which  is  equivalent  to  a  loss  of  energy. 


THEORY  OF  AIR  COMPRESSION  29 

It  is  obvious  that  in  the  second  case  the  heat  required  to  do 
work  must  come  from  some  source  other  than  the  compression 
work,  As  a  matter  of  fact,  it  is  heat  which  was  contained  in 
the  air  before  compression.  That  the  expansive  work  consumes 
some  of  this  heat  is  manifested  by  the  cold  created  around  the 
cylinders  of  an  engine  using  air  expansively. 

The  actual  temperatures  of  the  compressed  and  of  the  ex- 
panded air  under  various  conditions  may  be  determined  by 
applying  the  laws  and  formulas  given  in  preceding  articles. 

Example. — Let  a  volume  7=10  cu.  ft.  of  free  air  be  adiabatically 
compressed  in  one  stage  from  atmospheric  pressure  (P=  14.71b.  absolute) 
to  80  Ib.  gage  (Pi  =  94.7  Ib.  absolute);  the  initial  temperature  of  the  air 
being  60°  Fahr.  ( 7^  =  521  degrees  absolute). 

From  equation  (11),  Article  41,  we  deduce  the  absolute  temperature 
(Ti)  of  the  air  after  adiabatic  compression: 

T  _  T  /PA  ~»J  =  521  /94.7\  ••»  =  894.25°  absolute. 
\P)  \14.7/       =433.25°  Fahr. 

The  volume  Vi  into  which  the  air  has  been  compressed  under  adia- 
batic conditions,  we  find  from  equation  (13),  Article  41: 


If  we  cool  this  volume  V\  of  compressed  and  heated  air  to  initial  tem- 
perature of  60°  Fahr.  (T  =  521  degrees  absolute),  the  effect,  according 
to  Article  5,  will  be  a  decrease  of  pressure  under  constant  volume. 
Calling  the  new  pressure  P3,  we  find  same  by  applying  the  law  stated 
under  Article  19: 

P3     T 


m 

whence  P3=Pj  ~r  =  94.7  =  55.174  Ib.  absolute. 


The  volume  of  the  cooled  air  has,  of  course,  remained  the  same,  viz.  : 
2.664  cu.  ft. 

If  the  air,  occupying  a  volume  Vi  at  an  absolute  pressure  of  55.174 
Ib.  and  a  temperature  of  60°  Fahr.,  were  allowed  to  expand  adiabatic- 
ally down  to  atmospheric  pressure,  the  temperature  of  the  expanded 
air,  according  to  equation  (11),  Article  41,  would  be: 

*     -521  /  14-7  \  °'29  =  355.06  degrees  absolute. 
V55.174/       =  —105.94°  Fahr. 


30 


COMPRESSED  AIR    • 


and  from  equation  (13),  Article  41,  the  volume  V2  of  the  expanded  air 
would  be: 


6.8143  cu.  ft. 


2.664  - 


This  is  the  same  quantity  (weight)  of  atmospheric  air  we  started  out 
to  compress,  but,  being  so  much  colder  (  —  105.94°  Fahr.),  occupies  a 
smaller  volume  than  the  original  volume  of  10  cu.  ft.  If  we  now  heat 
this  cold  exhaust  air  to  initial  temperature  (60°  Fahr.),  under  constant 
pressure,  we  should  get  our  original  volume.  Applying  the  law  stated 
under  Article  18,  we  have- 

F,"r", 

whence  V=  V2  J  =  6.8143  ^  ~  =  10.00  cu.  ft. 

1  2  OOO.UO 

42.    Graphical     Illustration     of     Adiabatic    Compression. — 

Assume  a  cylinder  (Fig.  6)  whose  stroke  is  48  in.  and  which 


51  3|  31 

-a-\-er  gt-0.45»  OHIO.  VOL.-> 

.  li  i  §* 

-.ft-  -n  T  t1-0-812  °R|Q-  VOL- -> 


FIG.  6. — Diagram    Illustrating  Adiabatic  Compression  and  Delivery 


is  filled  with  air  at  atmospheric  pressure  at  a  temperature  of 
60°  Fahr.  and  having  a  piston  moving  in  it  in  the  direction  of 


THEORY  OF  AIR  COMPRESSION  31 

the  arrow.  Let  the  cylinder  be  connected  with  a  receiver  in 
which  the  pressure  is  six  atmospheres  or  73.5  Ib.  gage. 

If  we  move  the  piston  from  left  to  right  and  compress  the 
air  in  the  cylinder  to  two  atmospheres,  the  volume  will  not  be 
one-half  the  original  volume  (as  in  isothermal  compression)  but 
will  be  greater  than  one-half. 

From  column  3  of  Table  IV  we  find  that  the  volume  is  0.612 
times  the  original  volume,  hence  the  piston  will  be  at  a  point 
48- (0-612X48)  =  18-63  in.  from  the  left  end  of  the  cylinder. 
Thus  we  find  the  position  of  the  piston  at  a  pressure 

of  2  atmospheres  to  be  at  48 -(0.612X48)  =  18.63  in. 
of  3  atmospheres  to  be  at  48 -(0.459X48)  =25.97  in. 
of  4  atmospheres  to  be  at  48-  (0.374X48)  =30.05  in. 
of  5  atmospheres  to  be  at  48-  (0.319X48)  =32.69  in. 
of  6  atmospheres  to  be  at  48 -(0.281X48)  =34.51  in. 

from  the  left-hand  end  of  the  cylinder. 

43.  Construction  of  the  Adiabatic  Compression  Curve. — Draw 
a  horizontal  line  AD  which,  at  a  convenient  scale  represents  48 
in.,  and  mark  on  this  line  points  at  18.63,  25.97,  30.05,  32.69, 
and  34.51  in.  from  the  left  end;  then  draw  at  those  points  lines 
perpendicular  to  AD. 

On  these  lines  measure  off,  at  any  scale,  the  gage  pressures 
corresponding  to  the  stroke;  this  will  give  a  succession  of  points 
a,  6,  c,  d,  e,  f,  and  if  we  join  these  by  a  continuous  line  we  get  a 
curve  AB  which  represents  the  variations  of  air  pressure  during 
compression,  that  is,  the  gage  pressure  at  any  point  M  is  measured 
by  the  line  MN. 

The  curve  AB  is  known  as  the  curve  of  adiabatic  compression. 

If  we  took  any  number  of  intermediate  points  between  34.51 
and  48  in.  of  the  stroke,  the  pressure  would  always  be  73.5  Ib. 
gage,  and  consequently  a  line  connecting  these  points  will  be  a 
straight  line  BC  parallel  to  AD.  It  represents  the  period  of 
delivery  under  constant  pressure. 

WORK  OF  ADIABATIC  SINGLE-STAGE  COMPRESSION  AND 
DELIVERY 

44.  The  net  work  in  foot-pounds  performed  during  one  com- 
plete stroke  of  the  piston  in  compressing  adiabatically  a  volume 
Vi  of  free  air  from  an  absolute  pressure  PI  to  an  absolute  pressure 


32 


COMPRESSED  AIR 


Pz  and  in  delivering  the  compressed  air  which  now  occupies  a 
volume  V2,  under  constant  pressure  P2  into  the  receiver,  is 
obtained  in  the  identical  manner  as  has  been  shown  for  isothermal 
compression. 

Referring  to  Fig.  7,  net  work  performed  by  the  compressor  un- 
der the  conditions  named  is  Wn  =  144  X  (shaded  area  A  BCD)  ft.  Ib. 


B        DELIVERY         C 


FIG.  7. 

But  area  ABCD  =  area  MABR 
plus     area  BCOR 
minus    area  A  DOM 

Area,  MABR 
For  adiabatic  compression 


CVl 

'•    Pdv 

i/  Vt 


Hence 


area  MABR  = 


THEORY  OF  AIR  COMPRESSION  33 

=piFr    F-W 


1— n 
And  since  PiFin=P2F2n 

PiFi""^-1"" 
We  can  write  area  MABR  =  — 


l-n 
or,  area  MABR 


n-1 


Area    BCOR=P2V2 
Are&ADOM=P1V1 


Therefore     area  ABCD  +P2F2-P1F] 


n-l 


Substituting  we  get 

n-l 

ATeeiABCD  =  ^.PlV1\  (—}  "  -l]    and 

n —  1  L  vz  i/ 

n-l 

45.  Net  work  per  stroke  ^n  =  ^^PiF1[(p)  "  -l]    ft.-lb. 

in  which  PI  =  initial  absolute  pressure  in  pounds  per  square 

inch. 

PZ  =  final  absolute  pressure  in  pounds  per  square  inch. 
Fi  =  volume  of  free  air  in  cubic  feet  taken  into  the 

cylinder  per  stroke. 

n  =  exponent  adiabatic  compression  (1.406) 
3 


34  COMPRESSED  AIR 

46.  Mean  Gage  Pressure,  Adiabatic  Single-stage  Compres- 
sion and  Delivery.  —  The  mean  gage  pressure  in  pounds  per 
square  inch  in  single-stage  adiabatic  compression  and  delivery 
is  deduced  in  the  same  manner  as  shown  for  isothermal  com- 
pression. It  is 

Wn 
Pm  =  or 


Pm=r^1P1[(^)   "  -l]  Ib.  per  square  inch. 

Column  7  of  Table  III  gives  the  theoretical  mean  gage  pressure 
in  pounds  per  square  inch  for  adiabatic  single  stage  compression 
and  delivery. 

47.  Theoretical  Horse-power,  Adiabatic  Single-stage  Com- 
pression and  Delivery.  —  The  theoretical  horse-power  required 
to  compress  adiabatically  a  volume  Fi  of  free  air  in  one  stage 
from  an  absolute  pressure  PI  to  an  absolute  pressure  Pa  and  to 
deliver  the  compressed  air  into  the  receiver  at  a  constant  pres- 
sure P2  is  found  from  the  general  formula 

PLAN 


in  which   P  =  mean  gage  pressure  in  pounds  per  square  inch. 

L  =  length  of  stroke  in  feet. 

A  =  area  of  piston  in  square  inches. 

N  =  number  of  stroke.s  per  minute. 

If  by  Fi  we  designate  the  volume  of  free  air  in  cubic  feet  taken 
into  the  cylinder  per  minute,  we  have 


whence  LAW  =  144Fi.     Substituting  this  value  and  the  value 
Pm  for  P  in  our  formula  we  get 


!    in  r  /z\  1 

=  33-0^lT[(£)       -l]  (1) 

in  which  FI  =  volume  of  free  air  in  cubic  feet  to  be  compressed 

and  delivered  per  minute. 
PI  =  initial  absolute  pressure  in  pounds  per  square 

inch. 

Pt  =  terminal  pressure  in  pounds  per  square  inch. 
n  =  exponent  of  adiabatic  compression  (1.406) 


THEORY  OF  AIR  COMPRESSION  35 

A  glance  at  Fig.  7  shows  that  the  work  of  adiabatic  compression 
and  delivery  is  greater  than  that  of  isothermal  compression  and 
delivery.  In  actual  practice  the  indicator  card  from  an  air  cylin- 
der of  a  compressor  running  at  ordinary  speed,  shows  a  compres- 
sion line  approaching  the  adiabatic  curve  much  more  closely  than 
the  isothermal;  so  closely  that  in  making  computations  it  is 
usually  assumed  that  the  compression  has  been  adiabatic. 

Column  4  of  Table  V  gives  the  theoretical  horse-power  required 
for  adiabatic  single-stage  compression  and  delivery  of  1  cu.  ft. 
of  free  air  per  minute  (Fi  =  1.00)  at  sea  level. 

48.  Theoretical  horse-power,  single-stage  adiabatic  compres- 
sion and  delivery,  expressed  in  terms  of  absolute  temperatures 
and  weight  of  the  volume  of  air  to  be  compressed  and  delivered 
per  minute: 

According  to  Article  20,  equation  (5) : 

PiVl  =  RTl  (1) 

in  which  PI  =  absolute  pressure  of  air  in  pounds  per  square  foot. 
FI  =  volume  in  cubic  feet  of  1  Ib.  of  air  at  an  absolute 
pressure  PI  and  an  absolute  temperature  T\. 

From  equation  (7),  Article  20,  we  have: 

R  =  (KP-KV~)  =  184.8- 131.6  =53.2. 
From  Article  40,  equation  (1),  we  have: 


whence  Kv  =     T 

n 


(2) 
From  equation  (9)  in  Article  41  we  deduce: 


whence 

n         n 


Pi-VTi 

In  substituting  in  the  horse-power  formula,  Article  47,  the  value 
for  PiFi  as  given  in  equation  (1)  of  this  article,  it  must  be  remem- 
bered that  in  equation  (1)  the  pressure  PI  is  expressed  in  pounds 
per  square  foot  and  the  volume  FI  is  the  volume  in  cubic  feet  of 
1  Ib.  of  free  air,  whereas  in  the  horse-power  formula,  Article  47, 


36  COMPRESSED  AIR 

Pi  is  expressed  in  pounds  per  square  inch  and  V\  is  the  volume 
of  free  air  in  cubic  feet  to  be  compressed  per  minute.  Therefore 
if  we  wish  to  compress  adiabatically  and  deliver  w  pounds  of  free 
air  per  minute,  the  formula  becomes 


Introducing  value  of  R  from  (2) 

n(n-l)KpTl 


n(n-l)KpTl  r^-l 
Horse-power  =  w-^-^^—  \—t  f-  J 


Introducing  the  value  for  #p=184.8  we  get 

Theoretical  horse-power  =  0.0056  w[Tz-  T,\  (3) 

in  which  w  =  weight  of  the  number  of  cubic  feet  of  free  air  which 

are  to  be  compressed  and  delivered  per  minute. 
T2  =  final  absolute  temperature  of  compressed  air. 
Ti  =  initial,  absolute  temperature  of  free  air. 

Example.  —  Find  theoretical  horse-power  required  at  sea  level  to  com- 
press and  deliver  100  cu.  ft.  of  free  air  per  minute,  having  an  initial 
temperature  of  60°  Fahr.,  the  final  pressure  to  be  85  Ib.  gage. 

From  Article  23  we  find  the  weight  of  100  cu.  ft.  of  atmospheric  air 
at  60°  Fahr. 


From  equation  (11),  Article  41,  we  find  the  absolute  temperature  of 
the  air  after  compression: 


=  (60+461)  -BB9()8o 

Ti  =  (60+461)  =521° 

T2-Ti  =  387° 
Theoretical  horse-power  =  0.0056  X 7.64  X387  =  16.55 


THEORY  OF  AIR  COMPRESSION  37 

RELATION  BETWEEN  FINAL  PRESSURE  OF  A  GIVEN  QUANTITY 
OF  AIR  AND  THE  POWER  REQUIRED  TO  COMPRESS  TO  THAT 
PRESSURE 

49.  The  formulas  for  the  horse-power  required  to  compress 
and  deliver  a  certain  volume  of  free  air,  show  that  this  power 
is  not  directly  proportional  to  the  final  pressure.     For  in  the 

/P2\  -^- 
quotient    (j^j        the  pressures  are  absolute  pressures,  that  is, 

gage  plus  atmospheric  pressures. 

Doubling  the  gage  pressure  would  not  double  the  expression 
p 

rr  and  therefore  would  not  double  the  horse-power  required  to 

produce  that  pressure  in  the  air.     To  illustrate:     For  a  final  gage 
pressure  of  80  Ib. 

p         80+ 14  7 
The  quotient  p-  is  — J-  =  6.442 

for  160  lb. 

for  240  Ib.    £  is  - 17.33 

Referring  to  column  7  of  Table  V,  to  compress  100  cu.  ft.  of 
free  air  per  minute  in  two  stages  to  60  lb.  gage  requires  12.10 
h.p.  (theoretically).  To  compress  to  180  lb.,  which  is  three  times 
as  much,  only  requires  20.8  h.p.  which  is  less  than  twice  the  horse- 
power required  for  compression  to  60  lb. 

This  points  to  conditions  pertaining  to  compressed  air  which 
are  advantageous  in  the  transmission  and  final  use  in  air  engines 
as  pointed  out  under  Article  103. 

50.  Modified  Power  Values  for  Practical  Air  Compression 
Problems.— In  the  preceding  theoretical  formulas  no  allowance 
has  been  made  for  clearance,  the  heating  of  the  intake  air  in 
passing  through  the  valves,  and  the  friction  of  the  compressor. 

The  effect  of  the  first  two  items  on  the  consumption  of  power 
is  negligible  in  good  compressors.  The  additional  energy  required 
to  overcome  frictional  resistance  will  amount  in  well-designed 
compressors  to  from  7  to  15  per  cent,  of  the  theoretical  horse- 
power, depending  to  a  great  extent  on  the  care  that  is  taken 
with  the  machine. 

For  practical  compressor  computations  an  addition  of  15  per 
cent,  is  usually  made  to  the  horse-power  derived  from  the  theo- 
retical formulas. 


CHAPTER  V 

CLEARANCE,  VOLUMETRIC -EFFICIENCY,   CAPACITY,   SPEED, 
MECHANICAL-EFFICIENCY  OF  COMPRESSORS 

51.  Clearance. — This  is  the  space  enclosed  between  the  piston 
and  the  cylinder  head  at  the  end  of  the  stroke.  See  Fig.  3. 

The  clearance  space,  though  generally  a  source  of  loss,  is 
necessary  for  practical  reasons:  first,  to  avoid  danger  to  the 
cylinder  heads  by  allowing  space  for  the  water  that  may  accumu- 
late in  the  cylinders,  and  second,  to  provide  passage  sufficiently 
large  for  ready  admission  and  delivery  of  the  air. 

It  is  evident  that  the  clearance  volume  depends  upon  the  area 
of  the  piston.  In  short-stroke  cylinders  of  large  diameter  the 
clearance  volume  is  a  large  proportion  of  the  Piston  Displacement. 
The  latter  is  the  actual  volume  swept  through  by  the  piston  in 
one  stroke. 

Clearance  is  usually  expressed  as  a  ratio  between  clearance 
volume  and  cylinder  volume.  For  cylinders  of  same  diameter 
but  different  length  of  stroke,  the  ratio  is  larger  in  the  short- 
stroke  cylinder.  In  large,  up-to-date  compressors  it  varies  from 
1  to  2  per  cent.  It  is  much  more  in  very  small,  short-stroke 
machines. 

If  the  volume  swept  through  by  the  piston  in  one  stroke  is 
1000  cu.  in.  and  the  clearance  volume  is  20  cu.  in.  the  compressor 
has  2  per  cent,  clearance. 

62.  Losses  Due  to  Clearance.— If  the  discharge  pressure  is 
75  Ib.  gage  or  89.7  Ib.  absolute  and  the  initial  pressure  is  atmos- 
pheric pressure  at  sea  level,  that  is,  14.7  Ib.  absolute,  the  air  re- 
maining in  the  20  cu.  in.  clearance  space  will  expand  on  the 
return  stroke  of  the  piston  to  about  six  times  the  clearance 
volume,  or  to  120  cu.  in.  and  will,  therefore,  take  up  an  addi- 
tional 100  cu.  in.  from  the  in-take  cylinder.  That  is,  in  a 
cylinder  of  1000  cu.  in.  piston  displacement  the  piston  must 
travel  back  10  per  cent,  of  the  return  stroke  before  the  clearance 
air  has  expanded  to  atmospheric  pressure  and  before  the  atmos- 
pheric air  is  allowed  to  flow  into  the  cylinder. 
38 


MECHANICAL-EFFICIENCY  OF  COMPRESSORS  39 

The  actual  room  for  the  admission  of  new  free  air  is  therefore 
only  1000—100  =  900  cu.  in.,  or,  as  commonly  stated,  the  volu- 
metric efficiency  of  the  compressor  is  90  per  cent. 

Theoretically,  the  clearance  loss,  so  called,  is  one  of  volumetric 
efficiency  only  and  not  of  power.  For  although  this  air  re- 
quired work  in  compressing  it  to  receiver  pressure,  in  expanding 
it  helps  to  compress  the  air  on  the  other  side  of  the  piston. 
The  loss  of  power  due  to  loss  of  heat  during  expansion  of  the 
clearance  air  usually  is  a  negligible  quantity. 

In  practice,  a  loss  of  power  is  caused  by  clearance,  due  to  the 
fact  that,  in  order  to  deliver  a  definite  amount  of  air,  a  larger 
compressor,  consuming  more  power,  is  required. 

The  loss  of  volumetric  efficiency  due  to  clearance  is  less  for 
two-stage  than  for  single-stage  compression,  because  for  any 
given  capacity  the  low-pressure  cylinder  of  the  two-stage  machine 
is  practically  of  the  same  size  and  has  the  same  percentage  of 
clearance  as  the  cylinder  of  a  single-stage  machine.  But  the 
terminal  pressure  in  the  low-pressure  cylinder  of  the  two-stage 
machine  is  much  lower,  hence  the  expansion  of  the  clearance 
air  back  into  the  cylinder  volume  is  much  less,  and  as  a  conse- 
quence the  volumetric  efficiency  is  higher.  (See  Chapter  VI 
on  Compound  Compression.) 

63.  The  volumetric  efficiency  of  a  compressor  is  the  ratio  of 
the  volume  of  free  air  actually  admitted  and  compressed  in  the 
in-take  cylinder  to  the  piston  displacement. 

The  diagram  in  Fig.  8  represents  an  ideal  air  card,  in  which 

GA  is  the  admission  line. 
AB  is  the  compression  line. 
BC  is  the  delivery  line. 
CG  is  the  expansion  line. 

This  diagram  shows  graphically  the  loss  in  volumetric  efficiency 
due  to  clearance  and  also  that  due  to  imperfections  in  the  admis- 
sion of  free  air.  In  order  to  cause  the  outside  air  to  flow  into  the 
cylinder,  the  pressure  in  the  latter  must  be  less  than  the  atmos- 
pheric pressure;  the  admission  line  will  therefore  always  fall 
more  or  less  below  the  atmospheric  line  as  shown  exaggerated  on 
the  diagram.  If  the  in-take  areas  are  restricted,  the  drop  in 
pressure  may  become  considerable.  The  clearance  volume  is 
represented  by  the  lines  EF  =  CD. 


40  COMPRESSED  AIR 

FG  is  the  extra  volume  occupied  by  the  clearance  air  after 
expansion  and  if  there  were  no  other  losses,  the  volumetric 
efficiency  would  be  represented  by  the  line  AG.  But  on  the 
forward  stroke  the  piston  must  travel  a  distance  AR  before  the 
atmospheric  line  is  reached  and  before  actual  compression 
begins.  Hence  the  actual  volumetric  efficiency  in  the  case 
illustrated  by  the  diagram  is  represented  by  the  line  RG. 


C  3 


-PISTON  DISPLACEMEr< 


n 

II 


VACUUM 
-CLEARANCE 


FIG.  8. — Air  Card  of  a  Single-stage  Compressor. 

High-class  large  compressors  have  a  volumetric  efficiency  of 
over  90  per  cent.  In  small  single-stage  compressors  with 
insufficient  water  cooling,  restricted  inlet  areas,  and  leaking 
pistons,  the  volumetric  efficiency  will  be  found  much  below  the 
above  figure. 

It  will  be  observed  from  the  above  that,  in  making  calculations 
for  a  compressor  plant  to  furnish  a  certain  amount  of  free  air 
per  minute,  it  is  quite  important  to  make  due  allowance  for 
volumetric  efficiency.  In  installing  a  compressor  plant,  it  is  a 
wise  precaution  to  have  the  builder  guarantee  a  definite  minimum 
volumetric  efficiency. 

64.  Capacity. — Compressor  builders  frequently  call  the  free- 
air  capacity  of  their  machines  the  volume  swept  through  by  the 
piston,  without  making  any  deductions,  that  is,  if  the  area  of 
the  piston  is  2  sq.  ft.  and  the  latter  travels  500  ft.  per  minute, 
the  capacity  is  called  1000  cu.  ft.  per  minute. 

Now,  we  have  seen  that  if  the  clearance  of  a  compressor, 
compressing  to  75  Ib.  gage,  is  2  per  cent,  the  actual  capacity  is 
only  900  cu.  ft.  per  minute  and  if  1000  cu.  ft.  capacity  is  wanted  of 
the  same  compressor  it  must  be  speeded  up  to  555  ft.  per  minute. 


SPEED  OF  COMPRESSORS  41 

Clearance  is  one  of  the  factors  affecting  capacity.  Since  the 
volume  which  the  expanded  clearance  air  occupies,  increases  as 
the  pressure  increases,  it  follows  that  the  loss  in  capacity  by 
clearance  is  directly  proportional  to  the  pressure. 

Another  factor  affecting  compressor  capacity  is  the  condition 
of  the  air  taken  into  the  cylinder,  which  in  common  practice  of 
rating  capacities  is  assumed  to  be  at  atmospheric  pressure  and 
at  no  higher  temperature  than  the  outside  source  of  supply. 
Such  ideal  conditions  never  exist.  Even  with  unobstructed 
inlet  passages  air  will  not  flow  into  the  cylinder  without  some 
difference  in  pressure  to  force  it  in;  hence  the  air  taken  into  the 
cylinder  always  has  a  pressure  slightly  below  that  of  the  outside 
air.  Then  again,  the  entering  air,  coming  in  contact  with  the 
cylinder  walls  which  have  been  highly  heated  during  the  com- 
pression in  the  preceding  stroke,  is  heated  to  a  temperature 
higher  than  outside  temperature,  thereby  decreasing  in  density. 
As  a  consequence,  at  each  stroke  the  compressor  takes  in  a  volume 
of  air  which  weighs  less  than  the  same  volume  would  weigh 
had  it  remained  at  outside  temperature  and  pressure. 

The  temperature  of  a  given  volume  of  air  does  not  affect 
the  power  required  to  compress  and  deliver  that  volume,  it 
merely  expands  or  contracts  the  product. 

Table  VII  shows  the  effect  of  initial  in-take  temperature  upon 
the  efficiency  and  capacity  of  a  compressor. 

55.  Speed  of  Compressors. — From  what  has  been  said  concern- 
ing the  capacity  of  a  compressor,  it  might  be  assumed  that  this 
capacity  could  be  indefinitely  increased  by  increasing  the  piston 
speed.  This  is  true  to  a  certain  degree.  The  question  is,  where 
is  the  limit?  The  only  general  answer  that  can  be  given  is, 
when  it  does  no  longer  pay,  in  dollars  and  cents. 

Since  the  cost  of  compressing  air  must  depend  to  a  large  ex- 
tent on  industrial  conditions,  the  price  of  labor,  fuel,  supplies, 
etc.,  in  the  locality  where  the  air  is  to  be  used,  the  ultimate  speed 
of  an  air  compressor  is  usually  the  result  of  a  compromise  between 
first  cost,  operating  cost,  and  efficiency. 

There  are  other  factors  which  make  speeds  beyond  a  certain 
limit  objectionable.  It  has  been  shown  that  in  order  to  cause  the 
air  to  flow  into  the  in-take  cylinder,  there  must  be  a  difference 
between  the  pressures  inside  and  outside  of  the  cylinder.  The 
outside  pressure  being  normal  atmospheric  pressure,  the  pressure 
within  the  cylinder  on  the  in-take-stroke  must,  therefore,  always 


42  COMPRESSED  AIR 

be  something  less  than  this.  Increased  piston  speed  demands 
an  increase  of  velocity  at  which  the  air  must  flow  into  the  cylinder, 
and  this  in  its  turn  demands  a  greater  difference  between  the  in- 
side and  outside  pressure,  that  is,  a  reduced  pressure  in  the  in- 
take cylinder. 

From  the  diagram  in  Fig.  8  it  will  be  seen  that  a  large  drop  in 
pressure  of  the  in-take  air  below  atmospheric  pressure  means  a 
lengthening  of  the  distance  AR,  hence  a  decrease  of  volumetric 
efficiency. 

In  following  up  this  reasoning  it  becomes  evident  that  a  large 
increase  of  speed  will  usually  give  but  a  small  increase  in  delivery, 
besides  causing  a  rapid  wear  and  frequent  breakage  of  the  work- 
ing parts  of  the  machine,  to  say  nothing  of  the  increased  fric- 
tion which  in  its  turn  reduces  the  mechanical  efficiency  of  the 
compressor. 

Increased  speed,  furthermore,  means  increase  in  temperature 
because  the  air  is  rushed  through  the  cylinder  at  a  greater  velocity 
and  does  not  come  in  contact  with  the  water-jackets  long  enough 
to  be  cooled  to  any  great  extent.  This  rise  of  temperature  in- 
creases the  difficulty  of  lubrication  and,  if  carried  far  enough, 
it  may  reach  the  ignition  point  of  combustible  substances  in  the 
cylinders,  causing  an  explosion  with  all  the  expensive  delays  and 
repairs  incident  thereto. 

The  catalogues  of  compressor  builders  show  piston  speeds  of 
compressors  all  the  way  from  150  ft.  per  minute  for  small,  single- 
stage,  6-in.  stroke  machines  with  a  rated  capacity  of  30  cu.  ft. 
of  free  air  per  minute,  to  650  ft.  per  minute  for  a  large,  5-ft. 
stroke,  two-stage  compressor,  driven  by  a  compound  Corliss 
engine  with  a  rated  capacity  of  8000  cu.  ft.  of  free  air  per 
minute. 

56.  The  mechanical  efficiency  of  a  compressor  is  the  ratio  of 
the  power  ^theoretically  required  to  compress  and  deliver  a  given 
quantity  of  air  per  unit  of  time  to  the  power  actually  consumed. 

The  power  in  excess  of  the  theoretical  power  is  chiefly  re- 
quired to  overcome  frictional  resistances  of  the  machine,  for 
which  no  return  is  made  in  the  ultimate  use  of  the  compressed 
air.  It  therefore  is  a  loss  which  can  be  minimized  but  not  avoided 
altogether. 

The  amount  of  friction  is  dependent  both  on  the  design  of 
the  compressor  and  on  the  care  bestowed  upon  it  while  in 
operation. 


CHAPTER  VI 

TWO-STAGE  AND  MULTI-STAGE  COMPRESSION,  ALSO 
KNOWN  AS  COMPOUND  COMPRESSION 

THEORY 

57.  Single-stage,  isothermal  and  adiabatic  compression  of  air 
from  0  to  120  Ib.  gage  is  represented  in  Fig.  9  by  the  curves  AC 
and  AE  respectively. 

In  preceding  articles  it  was  explained  that  the  work  per- 
formed during  one  stroke  of  the  piston  is  represented  by  the 
area  in  the  diagram  to  the  right  of  the  compression  curve. 
It  was  also  explained  that  the  expenditure  of  energy  in  adiabatic 
compression  and  delivery  is  greater  than  in  isothermal  compres- 
sion and  delivery,  on  account  of  the  increase  in  volume,  due  to 
the  unchecked  rise  in  temperature. 

In  the  diagram,  Fig.  9,  the  area  A  DEC  B  A  therefore  stands 
for  the  waste  of  energy  in  adiabatic,  single-stage  compression 
and  delivery,  in  which  the  heat  of  compression  is  allowed  to 
remain  in  the  air.  This  heat  of  compression  represents  work 
done  upon  the  air  for  which  there  is  no  return,  since  during 
transmission  the  heat  is  all  lost  by  radiation  before  the  air  is 
used. 

The  problem  of  economy,  obviously,  becomes  one  of  abstract- 
ing the  heat  generated  in  the  air  during  the  process  of 
compression.  As  has  been  pointed  out,  this  is  partially  ac- 
complished by  water-jacketing  of  the  cylinder  walls.  But 
owing  to  the  short  interval  within  which  the  compression 
takes  place  and  the  comparatively  small  volume  of  air  actu- 
ally in  contact  with  the  cylinder  walls,  very  little  cooling  of 
the  air  occurs.  Cylinder  jackets  are,  however,  indispensable 
in  keeping  the  cylinder  walls  sufficiently  cool  for  effective 
lubrication,  and  in  the  prevention  of  cumulative  heating,  which 
in  extreme  cases  may  result  in  explosion. 

The  impossibility  of  proper  cooling  within  a  single  cylinder 
leads  to  the  alternative  of  discharging  the  air  from  one  cylinder, 
after  partial  compression  has  been  effected,  into  a  so-called 

43 


44 


COMPRESSED  AIR 


inter-cooler,  removing  the  heat  generated  during  the  first  com- 
pression, and  then  compressing  the  air  to  final  pressure  in  another 
cylinder.  This  method  of  accomplishing  compression  in  two 
steps  with  intermediate  cooling  is  called  two-stage  compression, 
or  when  repeated  one  or  more  times  for  high  pressures,  multi- 
stage compression.  See  Figs.  24  to  33  for  designs  of  modern 
two-  and  multi-stage  compressors. 

Referring  again  to  diagram  Fig.  9  and  assuming  the  com- 
pression in  each  cylinder  to  be  adiabatic,  the  compression 
curve  is  represented  by  the  interrupted  line  ADBH;  the  compres- 


EHC 


FIG.  9. — Diagram  Illustrating  Two-stage  Compression. 

sion  proceeds  adiabatically  in  the  first  or  low-pressure  cylinder 
to  D;  the  air  is  then  withdrawn  and  cooled  under  practically 
constant  pressure  in  a  suitable  vessel  called  an  inter-cooler,  until 
its  initial  temperature  is  reached  and  its  volume  is  reduced 
from  ID  to  IB;  with  good  inter-cooler  arrangement  it  may  be 
even  further  reduced;  it  is  then  introduced  into  a  second  or 
high-pressure  cylinder  and  compressed  adiabatically  as  before 
along  the  line  EH  to  the  final  pressure. 

As  before  noted,  the  energy  required  in  single-stage  com- 
pression and  discharge  of  a  given  quantity  of  air  under  isothermal 
conditions  is  proportional  to  the  shaded  area  ABCFG.  The 
additional  energy  required  in  two-stage  adiabatic  compression 
is  proportional  to  the  other  shaded  areas  ADB  and  ECU;  while 
the  loss  of  energy  in  adiabatic  single-stage  compression  and 
delivery  compared  with  isothermal  compression  and  delivery  is 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION 


45 


proportional  to  the  whole  area  ADECBA.  The  saving  effected 
by  two-stage  adiabatic  compression  and  delivery  is  therefore 
represented  by  the  unshaded  portion  DEHB. 

From  Table  V  it  appears  that  to  compress  1  cu.  ft.  of  free  air 
per  minute  to  100  Ib.  gage  and  deliver  it  at  that  pressure  into  the 
receiver,  requires  0.182  h.p.  in  single-stage  and  0.158  h.p.  in 
two-stage  compression  at  sea  level,  showing  a  saving  in  energy  of 
13  per  cent,  in  two-stage  compression. 

58.  Analysis  of  Two-stage  Compression.— Fig.  10  shows  the 
low-  and  high-pressure  air  cylinders  and  the  inter-cooler  of 


--Tniercooler.  C 


Discharge  fo 
Receiver  al 
120  Lb.  Gage. 


FIG.  10. — Diagram    Illustrating  Principle  of  Two-stage  Compression. 

an  Ingersoll-Rand  straight  line  steam-driven,  two-stage  air 
compressor. 

In  order  to  study  the  principle  of  operation  of  this  compressor 
we  must  assume  that  it  has  been  running  long  enough  to  bring 
about  normal  working  conditions;  viz.,  that  the  pressure  in  the 
receiver  has  reached  a  required  terminal  pressure  of,  say,  120  Ib. 
gage  and  that  the  inter-cooler  is  therefore  filled  with  air  at  about 
30  Ib.  gage. 

To  follow  the  air  through  its  various  stages  from  the  in-take 
to  the  discharge  during  one  stroke  of  the  piston,  let  it  be  assumed 
that  the  pistons  advance  from  right  to  left  as  indicated  by  the 
arrow  in  Fig.  10.  During  the  previous  stroke  from  left  to  right 


46  COMPRESSED  AIR 

the  inter-cooler  (C)  and  its  connections  (F  and  (?)  to  the  air 
cylinders  have  been  replenished  with  air  compressed  to  30  Ib. 
This  body  of  air  is  now  shut  off  from  both  cylinders  by  their  rela- 
tive valves  and  is  losing  the  greater  part  of  its  heat  and  some 
of  its  pressure  through  the  influence  of  the  circulating  cold  water 
in  the  inter-cooler.  The  loss  of  pressure  is  quickly  made  up  by 
the  equalizing  process  explained  below. 

During  the  first  part  of  the  return  stroke  from  right  to  left 
the  piston  (L)  in  the  low-pressure  cylinder  (A)  acts  only  on  the 
free  air  taken  in  on  the  previous  stroke,  while  the  high-pressure 
piston  (D)  is  engaged  in  compressing  to  the  terminal  pressure  the 
air  in  front  of  it,  which  has  been  admitted  on  the  previous  stroke 
from  the  inter-cooler  at  a  pressure  slightly  under  30  Ib. 

While  the  free  air  in  the  low-pressure  cylinder  (A )  is  being*com- 
pressed,  the  advance  of  the  piston  (D)  in  the  high-pressure 
cylinder  reduces  the  pressure  behind  it,  causing  the  high-pressure 
inlet  valves  (E)  to  open.  The  compressed  air  in  the  inter-cooler 
(C)  and  in  the  connections  (F  and  G)  now  rushes  into  the  high- 
pressure  cylinder  (B)  thereby  slightly  expanding  in  volume  and 
decreasing  in  pressure  until  the  pistons  have  reached  a  point 
somewhat  beyond  midstroke. 

When  the  pistons  have  passed  this  point,  the  air  pressure  in 
front  of  the  low-pressure  piston  (L)  rises  slightly  higher  than  that 
in  the  inter-cooler,  causing  the  low-pressure  delivery  valves  (M) 
to  open.  From  now  on  to  the  end  of  the  stroke  both  cylinders 
are  in  communication  with  each  other  through  the  inter-cooler. 

The  low-pressure  piston  now  acts  upon  the  entire  body  of  air 
contained  in  the  low-pressure  cylinder,  in  front  of  the  piston, 
in  the  inter-cooler,  in  the  connecting  passages  and  in  the  portion 
of  the  high-pressure  cylinder  behind  the  high-pressure  piston. 
At  the  same  time  the  air  in  front  of  the  high-pressure  piston 
is  delivered  into  the  receiver  at  constant  final  pressure. 

During  this  period  an  approximate  equalization  of  pressure  is 
established  throughout.  These  fluctuations  in  pressure  and  the 
final  equalization  of  pressure  which  take  place  during  each  stroke 
of  the  piston  may  be  observed  by  watching  the  movements  of 
the  hand  on  the  pressure  gage  (P)  and  from  the  indicator  diagrams 
taken  from  compressors  in  normal  operation.  (See  Chapter  VIII.) 

Referring  to  the  diagram,  Fig.  9,  the  saving  of  energy  in  two- 
stage  compression  was  explained  as  being  due  to  the  inter-cooler 
which  reduces  the  volume  ID  of  the  compressed  air,  coming 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION 


47 


from  the  low-pressure  cylinder,  to  a  volume  IB,  before  admitting 
it  into  the  second  or  high-pressure  cylinder. 

In  the  above  analysis  of  operation  no  mention  is  made  of  a 
reduction  in  volume.  The  reason  for  this  becomes  clear  when  it 
is  realized  that  the  air  which  enters  the  high-pressure  cylinder 
from  the  inter-cooler  is  not  the  identical  volume  of  air  which 
leaves  the  low-pressure  cylinder  at  that  moment,  but  is  a  quantity 
of  air  that  had  been  in  the  inter-cooler  long  enough  to  cool  down 
to  atmospheric  temperature  and,  being  cooled,  occupies  in  the 
inter-cooler  a  smaller  volume  than  it  did  when  it  entered  it.  The 
room  made  by  the  shrinkage  is  immediately  filled  at  the  other 
end  of  the  inter-cooler  by  a  quantity  of  hot  air  rushing  into  it 
from  the  low-pressure  cylinder  during  the  process  of  equalization 
mentioned  above. 

The  above  description  of  the  mode  of  operation  does  not 
strictly  apply  to  a  duplex  cross-compound  compressor  such  as 
shown  in  Fig.  28  because  there  the  pistons  work  with  one  crank 
90  degrees  in  advance  of  the  other,  and  at  certain  periods  in  the 
cycle  of  operation  travel  in  opposite  directions.  The  effect  of 
the  inter-cooler,  however,  is  practically  the  same  as  in  straight 
line  machines. 

RATIO  OF  COMPRESSION  IN  COMPOUND  OR  MULTI-STAGE 
COMPRESSION 

59.  The  ratio  of  compression  in  any  cylinder  of  a  compressor  is: 

terminal  absolute  pressure  in  that  cylinder 
initial  absolute  pressure  in  that  cylinder 


"° 


RCOOLER  2 


V8 


1 
T 

?@ 

II              II 

4-  © 

P.IU                 F 

i   Pi           p,   pa           p. 

1 

FIG.  11. 


© 


The  cylinders  of  a  multi-stage  compressor  are  dimensioned 
so  that  the  work  done  per  stroke  in  each  cylinder  is  as  nearly  as 


48  COMPRESSED  AIR 

possible  the  same,  thereby  equalizing  and  minimizing  the  strains 
on  the  machine. 

Let  1,  2,  3,  4  in  Fig.  11  represent  the  cylinders  of  a  multi-stage 
compressor,  and  let 

Pa  =  initial  absolute  pressure  in  cylinder  (1)  in  pounds  per  square 

inch, 
Pi  =  final  absolute  pressure  in  cylinder  (1)  in  pounds  per  square 

inch, 
=  initial  absolute  pressure  in  cylinder  (2)  in  pounds  per  square 

inch, 
P2  =  final  absolute  pressure  in  cylinder  (2)  in  pounds  per  square 

inch, 

=  initial  absolute  pressure  in  cylinder  (3)  in  pounds  per  square 
inch, 

&c. 

Va=  piston  displacement  in  cylinder  (1)  in  cubic  feet, 
Vz  =  piston  displacement  in  cylinder  (2)  in  cubic  feet, 

&c. 

then  the  net  work  per  stroke  of  adiabatic  compression  and  de- 
livery in  cylinder  (1)  is,  according  to  Article  45: 

*:-T=i''r.[&y-l]  foot-pounds.  (1) 

The  net  work  per  stroke  in  cylinder  (2)  is: 


j       -ll   foot-pounds.  (2) 

In  compound  compression  the  air  between  stages  is  supposed 
to  be  cooled  to  initial  temperature  under  constant  pressure; 
hence  the  volume  V2  of  air,  entering  cylinder  (2)  from  the  inter- 
cooler  at  an  absolute  pressure  PI  is  the  volume  which  cylinder 
(1)  would  deliver  per  stroke,  had  it  compressed  the  in- take 
air  Va  isothermally  during  that  stroke  instead  of  adiabatically 
to  the  pressure  PL  From  this  it  follows  that  in  stage  compres- 
sion with  perfect  inter-cooling  between  stages,  Boyle's  law 
(Article  15)  becomes  applicable: 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION  49 

Substituting  this  value  in  equation  (2)  we  get 
Net  work  per  stroke  in  cylinder  2: 

~l     foot-pounds  (3) 


Net  work  per  stroke  in  cylinder  1  : 


A  glance  at  equations  (3)  and  (1)   shows  that  Wn"  becomes 

•p 
equal  to  Wn'  when  the  ratio  of  compression  p-  in  cylinder  (2) 

r> 

becomes  equal  to  the  ratio  of  compression  ~  in  cylinder  (1). 

fa 

This  leads  to  the  general  conclusion:  In  order  that  the  work 
per  stroke  in  each  cylinder  of  a  compound  compressor  be  theo- 
retically the  same,  the  following  relations  between  the  terminal 
and  initial  pressures  in  the  various  cylinders  must  exist: 

A  ^^^  etc 

Pa  ~Pl~P2~P3 

60.  For  two-stage  compression  we  have  : 

ft  .5l  (1) 

Pa~Pi 

Dividing  by  Pa  JT*=W 

fa          -to 

Whence  g=g=^  (2) 

This  shows  that  the  ratio  of  compression  in  each  of  the  two 
cylinders  must  be  equal  to  the  square  root  of  the  total  ratio  of 
compression;  the  total  ratio  being  the  ratio  between  the  final 
pressure  in  cylinder  (2)  and  the  initial  pressure  in  cylinder  (1). 

From  equation  (2)  we  get: 

=  <P<f*  (3) 


50  COMPRESSED  AIR 

61.  For  three-stage  compression  we  have : 

*_*-?!  (1) 

P«~Pi~P2 

Whence  ^2=^Pa 

Substituting  this  value  in  (1) 

pi^'A2"0 

Dividing  by  Pa2, 

P«»~P« 

Whence  F  =  Pi =  Pz =  \  P« 

That  is,  the  ratio  of  compression  in  each  of  the  three  cylinders 
must  be  equal  to  the  cube  root  of  the  total  ratio  of  compression. 
From  equation  (2)  we  get 

PJ  =  Vp~2p,  (3) 

Pa 

62.  For  four-stage  compression  we  would  find 
whence  Pi  =  Pa^  hr  =  V^P^Pi  (2) 


(3) 
(4) 


CYLINDER  DIAMETERS  OF  MULTI-STAGE  COMPRESSORS 

63.  The  cylinders  of  a  multi-stage  compressor  are  proportioned 
in  accordance  with  the  initial  volume  Va  of  free  air  to  be  com- 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION  51 

pressed  per  stroke  or  per  minute  and  the  ratio  of  compression  in 
each  cylinder,  as  obtained  from  the  formulas  in  Articles  60, 
61  and  62. 

In  compressed-air  computations  the  volume  Va  to  be  com- 
pressed per  stroke  or  per  minute  is  usually  given;  the  length  of 
the  stroke  is  made  the  same  in  all  cylinders;  the  number  of 
strokes  per  minute  is  chosen  with  reference  to  the  type  of  com- 
pressor desired  and  the  number  of  cubic  feet  of  air  required  per 
minute. 

Referring  to  Fig.  11 : 

Let  Va  =  volume  of  free  air  in  cubic  feet,  taken  into  cylinder  (1) 

per  stroke, 

F2  =  volume  which  the  air  discharged  from  cylinder  (1) 
occupies  at  a  pressure  PI  after  being  cooled  to  initial 
temperature, 

=  piston  displacement  of  cylinder  (2), 
F3  =  volume  which  the  air  discharged  from  cylinder  (2) 
occupies  at  a  pressure  P%  after  being  cooled  to  initial 
temperature, 
=  piston  displacement  of  cylinder  (3), 

&c. 

di  =  diameter  of  cylinder  (1)  in  inches, 
d2  =  diameter  of  cylinder  (2)  in  inches, 

&c. 

A  =  area  of  piston  in  cylinder  (1)  in  square  inches, 
L  =  length  of  stroke  in  inches, 

A      L     0.7854di«L 
then  y°=T44XT2=~~l728~~ 

IV 

whence  d\  =  47*/-=?  inches. 

Having  thus  determined  the  diameter  di  of  the  in-take  or 
low-pressure  cylinder  (1),  the  diameters  of  the  other  cylinders  are 
found  as  follows: 

The  length  of  stroke  being  the  same  for  each  cylinder,  the 
volumes  of  the  cylinders  are  in  the  ratio  of  the  squares  of  their 
diameters.  Assuming  complete  inter-cooling  between  stages, 
the  volumes  according  to  Article  16,  are  also  in  the  inverse  ratio 
of  the  pressures.  In  this  connection  it  must  be  remembered 


52  COMPRESSED  AIR 

that  volume  V^,  for  instance,  is  the  volume  which  the  air  discharged 
from  cylinder  (1)   would  occupy  after  being  cooled  to  initial 
temperature  under  constant  pressure  PI. 
Referring  to  Fig.  11  we  would  have 

dS  =  V?     Pa     ±_ 
di2     Va     P!    Pi 

Pa 

hence 

square  of  diam.  of  one  cylinder  _  1  __  1 

square  of  diam.  of  preceding  cyl.  "ratio  of  compr.  in  each  cyf.  ~~  r 

From  Articles  60  to  62  we  have: 
For  two-stage  compression: 


For  three-stage  compression: 


\P 
For  four-stage  compression: 


Therefore: 

Cylinder  Diameters 

64.  Cylinder  Diameters  for  a  Two-stage  Compressor.— 

di  =47*  I    °  inches 

dJ_(P.\*  ,P  vl 

di2  ~  \P2  /  whence      d2  =  rf,     /       inches 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION  53 

65.  Cylinder  Diameters  for  a  Three-stage  Compressor.  — 

rf1  =  47J~-  inches 


whence     d^=di  inches 


(Pa  \  ®          /Pa  \  •  /P    \  ^ 

di  (^-  )    X  (^-J        whence      d3  =  di  (~)    inche 


66.  Cylinder  Diameters  for  a  Four-stage  Compressor.  — 

~  • 
inches 


(P 
^7 


whence 


/P    \  ~S 

whence 


- 

inches 


inches 


P    \  ^        /p   \  ** 

XI  -1         whence 


p    \  ^ 

L      inches 


67.  The  volumetric  efficiency  of  the  compressor  only  affects 
cylinder  (1).  Therefore  in  the  above  calculations  of  the  diam- 
eters di,  dz,  ds,  etc.,  the  value  d\  as  given  in  the  formula  will 
be  used,  and  the  final  value  of  di  will  be  di  as  found  by  the  formula, 
plus  an  allowance,  depending  on  the  volumetric  efficiency 
of  the  compressor. 

Example  a.  —  What  should  be  the  diameters  of  the  air-cylinders  of  a 
three-stage  compressor  to  furnish  300  cu.  ft.  of  free  air  per  minute, 
compressed  to  300  Ib.  gage? 


54  COMPRESSED  AIR 

Length  of  stroke  L=  16  in. 
Number  of  r.p.m.  =  135 
Volumetric  efficiency  =  85  per  cent. 
Diameter  of  piston  rod  =  2  1/2  in. 

b.  What  is  the  terminal  pressure  in  each  of  the  cylinders  and  what 
is  the  ratio  of  compression  in  each  cylinder? 

Solution  a.  The  number  of  revolutions  being  135,  the  number  of 
strokes  per  minute  is  270.  Hence  the  volume  of  free  air  taken  into  the 
cylinder  per  stroke  is: 


To  which  must  be  added,  volume  of  piston  rod' 


Hence  Fa  =  1.11+0.045=1.155  cu.  ft. 

And      dv    =47X/k1^5=12.63in. 
^     16 

(       14J      ]*-' 
dz   =dl\  300+ 14777    =  7'58  m* 

/      147       \* 
d*   =dl\300+147/    =4'55in- 

The'diameter  di  of  the  in-take  cylinder  must  be  increased  to  allow  for 
a  volumetric  efficiency  of  85  per  cent. 

Calling  the  final  diameter  of  the  in-take  cylinder  x  we  have: 

x2  _100 
dS~  85 

Whence  x  =  d1^/100=  12.63X1.085=  13.71  in. 

Solution  b.     From  Article  61,  terminal  pressure  in 


Cylinder  (1)    P1  =  X/14.72X314.7  =  40.81  Ib.  absolute 

=  26.11  Ib.  gage. 

Cylinder  (2)    P2  =  ^14.7X314.7*  =  1 13.34  Ib.  absolute. 

=   98.64  Ib.  gage. 
Cylinder  (3)    P3  =314.7    Ib.  absolute 

=  300.00  Ib.  gage. 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION  55 

Ratio  of  compression  in  each  cylinder: 


In  cylinder  (1)  =2.78 

In  cylinder  (2)  ^|£      =2.78 

In  cylinder  (3)  =2.78 


THEORETICAL  HORSE-POWER,  COMPOUND  COMPRESSION  AND 
DELIVERY 

68.  For  two-stage  compression,  the  theoretical  horse-power 
required  to  compress  adiabatically  a  volume  of  free  air  in  cubic 
feet  per  minute  from  an  initial  absolute  pressure  Pa  to  a  final 
pressure  PZ  and  deliver  it  at  that  pressure  into  the  receiver,  is 
the  sum  of  the  horse-power  required  in  each  of  the  two  cylinders. 
In  Article  60  it  was  shown  that  for  a  two-stage  compressor  the 
ratio  of  compression  in  each  cylinder  must  be  equal  to  the  square 
root  of  the  total  ratio  of  compression,  that  is: 


The  horse-power  required  in  each  of  the  two  cylinders  is  there- 
fore 


Horse-power  =  33j000(n-l) 

And  for  the  two  cylinders  the  horse-power  is  just  twice  that 
amount. 

69.  Theoretical    horse-power  —  two-stage    compression    and 
delivery. 

144nFoPa    r/PoX^       1 
Horse-power  =  233j00()  (n_1}  |_  \pj 

in  which  Va  =  volume  of  free  air  in  cubic  feet  per  minute,  taken 

into  the  low-pressure  cylinder  (1). 
Pa  =  initial  absolute  pressure  in  pounds  per  square  inch 
in  the  low-pressure  cylinder  (1). 


56  COMPRESSED  AIR 

P2  =  final  absolute  pressure  in  pounds  per  square  inch 

in  the  high-pressure  cylinder  (2). 
n  =  exponent  of  adiabatic  compression  (=1.406). 
In  the  same  manner  we  find  for: 


70.  Three-stage  compression 

144n7.P. 


Horse-power  = 
71.  Four-stage  compression 

144n70Pa 


,1 


Horse-power  = 


(n_ 


The  theoretical  mean  gage  pressure  in  pounds  per  square  inch 
is  for: 

72.  Two-stage  compression 


73.  Three-stage  compression 


Columns  7,  10,  and  13  of  Table  V  give  the  theoretical  horse- 
power required  at  sea  level  to  compress  adiabatically  and  deliver 
1  cu.  ft.  of  free  air  per  minute  by  two-,  three-,  and  four-stage 
compression. 

FINAL  VOLUMES  AND  TEMPERATURES  OF  AIR  IN  STAGE 
COMPRESSION 

73A.  Two-stage  Compression. — On  its  passage  from  the 
low-pressure  cylinder  via  the  intercooler  to  the  high-pressure 
cylinder,  the  air  is  cooled  under  constant  pressure  to  initial 
temperature.  On  entering  the  high-pressure  cylinder  its  volume 
Vi  will  therefore  be  equal  to  a  volume,  the  intake-air  Va  would 
occupy  had  it  been  compressed  isothermally  in  the  low-pressure 
cylinder.  According  to  Boyle's  law  this  volume  is 

v,-v  (i) 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION  57 

In  the  high-pressure  cylinder  volume  Vi  is  compressed  adia- 
batically  to  a  volume  F2  and  to  an  absolute  pressure  P2- 
i 

Therefore         £=@  = 

Introducing  value  of  Vi  from  (1)  and  value 
Pl  =  VPaPzfrom  (3),  Art.  60, 

ro+l 

we  get  F2=Fa(^)2'  (2) 

The  absolute  temperature  of  the  discharge  air  will  be  the 
same  as  temperature  TI  of  the  air  when  leaving  the  low-pressure 
cylinder,  the  ratio  of  compression  being  the  same  in  both  cylinders. 

According  to  (11),  Art.  41 


Introducing 
we  get 

By  similar  deductions  we  obtain  analogous  values  for  three- 
and  four-stage  compression  as  indicated  in  Table  VIII. 

74.  Modified  Power  Values  for  Practical  Problems.  —  In  the 
preceding  theoretical  formulas   no   allowance   has   been   made 
for  clearance,  the  heating  of  the  in-take  air  and  the  friction  of 
the  compressor.     As  previously  stated,  the  first  two  items  are 
negligible  as  far  as  they  affect  power  consumption.     For  fric- 
tion an  additional  allowance  of  from  7  to  15  per  cent,  of  the 
theoretical  horse-power  is  usually  made  in   practical  compres- 
sor calculations. 

75.  Advantages  of  Multi-stage  Compression.  —  The  principal 
advantage  of  compound  or  multi-stage  compression  over  single- 
stage  compression  lies  in  the  saving  of  energy  by  reducing  the 
heat  of  compression  as  pointed  out  above.     Other  important 
advantages    due    to    compounding    may    be    summed   up    as 
follows  : 

a.  Reduced  Strain  on  Machine.  —  This  will  appear  from  the 
following  illustration: 

Consider  two  compressors,  compressing  air  to  120  Ib.  gage, 
one  compressor  having  a  single  air  cylinder  of  the  usual  pattern, 


58  COMPRESSED  AIR 

the  other  having  compound  cylinders.  With  a  piston  of  100 
sq.  in.  in  area,  the  maximum  resistance  which  the  single-stage 
compressor  must  overcome,  would  be  12,000  Ib. 

Let  us  now  consider  a  two-stage  compressor  in  which  the  area 
of  the  low-pressure  cylinder  piston  is  again  100  sq.  in.  and  that 
of  the  high-pressure  cylinder  one-third,  or  33  1/3  sq.  in.  In 
the  low-pressure  cylinder  the  air  is  compressed  to  about  30  Ib. 
Since  this  pressure  of  30  Ib.  acts  on  the  back  of  the  piston  in  the 
high-pressure  cylinder,  it  assists  the  machine,  and  the  net  re- 
sistance of  forcing  the  air  from  the  larger  into  the  smaller  cylinder 
is  equal  to  the  difference  in  the  areas  of  the  two  pistons  (which  is 
66  2/3  sq.  in.)  multiplied  by  30  Ib.  This  equals  2000  Ib. 

In  the  smaller  or  high-pressure  cylinder  the  maximum  re- 
sistance to  overcome  is  100X33  1/3  =  3333  Ib.,  and  the  sum 
of  the  two  resistances  at  the  time  of  greatest  effort  in  the  two- 
stage  compressor  is  5333  Ib.  as  compared  with  12,000  Ib.  in  the 
single-stage  compressor,  representing  a  reduction  in  strains  of 
more  than  one-half. 

b.  Improved  Steam  Economy. — The  more  equable  distribution 
of  the  load  throughout  the  stroke  greatly  reduces  the  danger  of 
centering.     This  permits  an  earlier  cut-off  in  the  steam  cylinder, 
resulting  in  a  greater  steam  expansion.     With  properly  designed 
inter-coolers  the  piston  speed  can  be  increased  without  danger 
of  overheating  the  cylinders.     Increased  piston  speed  is  in  itself 
a  factor  in  steam  economy,   since  it  reduces  leakage  and  con- 
densation in  the  steam  end  of  the  compressor. 

c.  Increased    Safety    and    Ease    of  Lubrication. — When    high 
final  temperatures  prevail,  part  of  the  lubricating  oil  vaporizes, 
and  the  wear  on  piston  and  cylinder  becomes  rapid.     Under 
exceptional  circumstances  the  combination  of  air  and  oil  vapor 
and  other  combustibles  may  reach  the  proportions  of  an  explo- 
sive mixture  and,  if  the  compression  temperature  reaches  its 
ignition  point,  an  explosion  may  result.     Such  accidents  are, 
however,  very  rare  even  in  single-stage  work;  in  multi-stage 
compression,  with  proper  inter-cooling  and  proper  attention  they 
are  practically  impossible. 

If  the  work  of  compression  has  been  divided  equally  between 
the  cylinders  by  a  correct  proportioning  of  their  diameters, 
and  if  the  inter-coolers  are  properly  designed,  the  final  tem- 
perature in  each  cylinder  will  be  the  same,  and  it  will  be  much 
lower  than  if  compression  was  completed  in  one  cylinder.  To 
illustrate: 


TWO-STAGE  AND  MULTI-STAGE  COMPRESSION  59 

In  compressing  air  at  atmospheric  temperature  of  60°  Fahr. 
to  100  Ib.  pressure  in  a  two-stage  compressor,  the  air  is  com- 
pressed from  atmospheric  pressure  to  26  1/2  Ib.  in  the  in-take 
or  low-pressure  cylinder,  and  is  delivered  to  the  inter-cooler  at 
this  pressure  and  at  240°  Fahr.  If  all  the  heat  of  compression  is 
taken  out  by  the  inter-cooler,  it  is  admitted  to  the  high-pressure 
cylinder  at  atmospheric  temperature  and  is  then  compressed 
from  26  1/2  Ib.  to  100  Ib.  and  delivered  to  the  receiver  at  a  tem- 
perature of  240°  Fahr.  (Radiation  and  cooling  by  water-jack- 
ets not  considered.) 

In  a  single-stage  compressor  the  air  is  compressed  from 
atmospheric  pressure  to  100  Ib.  in  one  cylinder  and  reaches  the 
receiver  at  a  temperature  of  482°  Fahr. 

d.  Greater  Effective  Capacity  in  Free  Air. — Clearance  loss  in 
an  air  compressor  is  principally  a  loss  in  capacity,  and  affects 
only  the  in-take  cylinder;  it  increases  with  the  terminal  pressure 
in  this  cylinder.     Since  in  compound  compression  the  terminal 
pressure  in  the  low-pressure  cylinder  is  much  lower  than  in  the 
single-stage  machine,  the  air  confined  in  the  clearance  spaces, 
when  expanded  down  to  atmospheric  pressure,  occupies  com- 
paratively little  space.     Consequently  the  in-flow  of  air  through 
the  suction  or  inlet  valves  begins  at  an  earlier  point  in  the  stroke 
than  it  would  in  the  single-stage  compressor,  which  results  in  a 
greater    volumetric    efficiency    of    the    compound    compressor. 
(See  discussion  of  indicator  cards  in  Chapter  VIII.) 

e.  Dryer  Air. — The  air  delivered  by  a  compound  compressor 
is  dryer  than  that  furnished  by  a  single  cylinder.     Under  con- 
stant pressure,  the  power  of  air  to  hold  vapor  decreases  with  its 
temperature,  and  during  its  passage  through  the  inter-cooler 
much  of  the  original  moisture  in  the  air  is  precipitated.     Conse- 
quently less  trouble  is  experienced  from  condensation  in  the 
discharge  pipe,  and  the  danger  of  freezing  up  the  exhaust  ports 
of  machines  using  compressed  air  is  greatly  reduced. 

76.  When  to  use  Two-  and  Multi-stage  Compression. — 
Below  and  up  to  60  or  70  Ib.  terminal  pressure,  the  adiabetic 
loss  is  comparatively  trival,  and  within  this  limit  and  at  low 
altitudes,  single-stage  compressors  are  commonly  employed. 
Between  60  and  100  Ib.,  the  amount  of  fuel  is  usually  the  deter- 
mining factor,  though  high  altitude  may  also  enter  into  the  ques- 
tion. Above  100  Ib.  both  safety  and  economy  speak  for  two- 
stage  and  above  500  Ib.,  for  multi-stage  compressors. 


CHAPTER  VII 
EFFECT  OF  ALTITUDE  ON  AIR  COMPRESSION 

77.  Volumetric  Efficiency.  —  The  volumetric  efficiency  of  a  com- 
pressor, expressed  in  terms  of  free  air,  is  the  same  at  all  altitudes 
because  the  piston  displacement  in  a  cylinder  of  a  given  size  is 
the  same.  But  the  volumetric  efficiency,  expressed  in  terms  of 
compressed  air,  decreases  as  the  altitude  increases. 

Since  the  density  and  hence  the  atmospheric  pressure  de- 
creases with  the  altitude,  a  compressor  located  at  an  altitude 
above  sea  level  takes  in  at  each  revolution  a  smaller  weight  of 
air  at  a  lower  pressure  than  at  sea  level,  and  the  early  part  of  each 
stroke  is  occupied  in  compressing  the  air  from  this  lower  pressure 
up  to  the  sea  level  pressure.  In  other  words,  the  free  air  taken 
into  a  cylinder  per  stroke  being  less  dense  at  an  altitude  (due  to 
lower  initial  atmospheric  pressure)  it  will  be  compressed  into  a 
smaller  space  for  a  given  terminal  pressure. 

Example.  —  Five-hundred  cubic  feet  of  air  at  atmospheric  pressure 
at  sea  level  (14.7  lb.),  compressed  isothermally  to  80  Ib.  gage,  occupies 
a  volume  of 


From  Table  VI  the  atmospheric  pressure  at  an  altitude  of  10,000  ft. 
is  10.07  lb.  and  500  cu.  ft.  of  air,  compressed  isothermally  to  80  lb.  gage 
at  that  altitude  would  occupy  a  volume  of 


That  is,  the  volumetric  efficiency  in  terms  of  compressed  air  of  a  com- 
pressor performing  the  above  work  at  an  altitude  of  10,000  ft.  is  only 
72  per  cent,  of  what  it  would  be  at  sea  level. 

In  order,  therefore,  that  an  air  compressor  at  an  altitude  may  deliver 
a  volume  of  compressed  air  per  stroke  equal  to  that  which  it  would 
deliver  at  sea  level,  the  in-take  cylinder  of  the  altitude  compressor  must 
be  proportionally  larger  than  that  of  a  compressor  at  sea  level. 

78.  Multipliers  for  Altitude  Computations.—  Referring  to  the 
preceding  example,  multipliers  may  be  computed  for  determin- 

60 


EFFECT  OF  ALTITUDE  ON  AIR  COMPRESSION  61 

ing  the  volume  of  free  air  at  various  altitudes  which,  when  com- 
pressed to  various  pressures,  is  equivalent  in  effect  'to  a  given 
volume  of  free  air  compressed  to  the  same  pressure  at  sea  level. 

Let     V  =  a  certain  number  of  cubic  feet  of  atmospheric  air  to 
be  compressed  simultaneously  at  sea  level  and  at  an 
elevation  above  sea  level, 
P  a  =  absolute  pressure  of  atmospheric  air  in  ibs.  per  square 

inch  at  sea  level  (14.75  lb.), 
PI  =  absolute  pressure  of  atmospheric  air  in  Ibs.  per  square 

inch  at  the  given  elevation, 
p  =  gage  pressure  to  which  air  is  being  compressed, 

then  the  volume  Vi  which  the  air  occupies  after  being  compressed 
to  p  pounds  gage  at  sea  level: 

Pa 


And  the  volume  F2  which  the  air  occupies  after  being  compressed 
to  p  pounds  gage  at  the  elevation: 


In  order  that  Vz  may  be  equal  to  Vi  it  must  be  multiplied  by 
a  multiplier  "M"  which  we  find  as  follows: 


Substituting  values 


p+P0 

jr- 


Example.  —  What  is  the  multiplier  for  a  volume  of  air  at  5000  ft. 
elevation  and  for  a  pressure  of  80  lb.  gage.     (See  Table  VI.) 


J80J-  12.20) 
'     Pi(P+Pa)       12.20  (80+14.75) 

If  for  instance  we  wish  to  know  the  volume  of  free  air  which  after 
being  compressed  to  80  lb.  gage  at  an  altitude  of  5000  ft.,  has  the  same 
effect  as,  say  100  cu.  ft.  of  air  compressed  to  80  lb.  gage  at  sea  level,  we 
find  it  by  multiplying  100  by  1.178. 
Thus,  100X1.178  =  117.8  cu.  ft. 


62  COMPRESSED  AIR 

79.  Power  Required  for  Altitude  Compressors.  —  To  compress 
a  given  volume  of  free  air  taken  in  by  a  compressor  of  given  size 
to  a  given  terminal  pressure  takes  less  power  at  an  altitude  than 
at  sea  level.  The  air  being  lighter  and  less  dense,  its  volume  at 
the  desired  terminal  pressure  will  be  smaller,  that  is,  the  final 
pressure  is  reached  at  a  later  point  in  the  stroke.  Hence  the  mean 
pressure  is  less  and  so  is  the  total  power  required  to  compress  the 
quantity  of  air  taken  into  the  cylinder. 

But,  in  order  to  produce  at  an  altitude  a  quantity  of  com- 
pressed air  which  is  equivalent  in  effect  to  air  at  sea  level,  more 
power  is  required,  because  the  reduction  in  power  referred  to 
above  is  not  proportional  to  the  increase  in  volume  necessary  to 
equal  sea-level  performance. 

Example.  —  Using  formula,  Article  68,  we  find  that  to  compress  by 
two-stage  compression  100  cu.  ft.  of  free  air  per  minute  at  sea-level 
pressure  (14.7  Ib.)  to  100  Ib.  gage  and  deliver  it  into  the  receiver  re- 
quires 15.80  h.p.  At  an  altitude  of  10,000  ft.,  where  the  atmospheric 
pressure  is  10.07  Ib.,  it  would  require  only  12.50  h.p. 

But  from  Table  VI,  a  quantity  of  air  which  at  an  elevation  of  10,000 
ft.  is  the  equivalent  of  100  cu.  ft.  of  free  air  at  sea  level  would  occupy 
a  volume  of  140.4  cu.  ft.  To  compress  this  quantity  to  100  Ib.  gage  and 
deliver  it  into  the  receiver  would  require: 


12.50  =  17.55  h.p. 

This  shows  that  in  this  case  1.75  additional  horse-power  are  required 
at  10,000  ft.  elevation  to  produce  the  same  effect  as  at  sea  level. 

80.  Stage  Compression  at  High  Altitudes.—  From  what  has 
been  said  of  the  effect  of  altitude  on  air  compression,  it  becomes 
evident  that  stage  compression  at  altitudes  results  in  even  larger 
percentage  of  saving  of  power  than  is  possible  at  sea  level. 

Referring  to  Table  V,  it  requires  0.182  h.p.  at  sea  level  to  com- 
press in  one  stage  1  cu.  ft.  of  free  air  per  minute  to  100  Ib.  gage 
and  deliver  it  into  the  receiver.  Two-stage  compression  would 
consume  only  0.158  h.p.  which  means  a  saving  of  0.024  h.p.  or  of 
13  per  cent,  in  favor  of  two-stage  compression. 

At  9000  ft.  above  sea  level  the  equivalent  of  1  cu.  ft.  of  air 
at  sea  level  is  1.356  cu.  ft.  and  the  atmospheric  pressure  is  10.46 
Ib.  (from  Table  VI).  Horse-power  required  to  compress  1.356 
cu.  ft.  of  free  air  per  minute  to  100  Ib.  gage  at  9000  ft.  elevation 
and  deliver  it  into  the  receiver: 


EFFECT  OF  ALTITUDE  ON  AIR  COMPRESSION  63 

For  single-stage  compression,     0.21  h.p.  (from  Article  47) 
For  two-stage  compression,        0.17  h.p.  (from  Article  68) 

which  means  a  saving  of  0.04  h.p.  or  of  19  per  cent,  in  favor  of 
two-stage  compression  at  an  altitude  of  9000  ft. 

81.  It  has  been  pointed  out  heretofore  that  the  volumetric 
efficiency  of  a  compressor  is  higher  in  two-stage  than  in  single- 
stage  compression,  owing  to  the  smaller  volume  which  the  ex- 
panded clearance  air  occupies.  This  volume  being  a  function 
of  the  ratio  of  compression,  it  follows  that  at  high  altitudes, 
stage  compression  can  be  profitably  used  for  lower  terminal  pres- 
sures than  is  customary  at  sea  level. 

To  illustrate:  The  ration  of  compression  at  sea  level  in  com- 
pressing to  90  Ib.  gage  is 

90+14.7 
14.7 

The  same  ratio  would  obtain  at  an  elevation  of  10,000  ft.  in 
compressing  to  61.63  Ib.  gage;  for 

61.63+10.07 


10.07 


=  7.12, 


which  means  that,  if  it  pays  to  use  two-stage  compression  at  sea 
level  in  order  to  reduce  clearance  losses  when  compressing  to  90 
Ib.  gage,  it  would  pay  to  do  so  at  10,000  ft.  elevation,  when  com- 
pressing to  62  Ib.  gage. 

The  theoretical  power  required  to  compress  a  certain  quantity 
of  air  at  an  altitude  above  sea  level  can  be  deduced  from  the 
formulas  for  the  mean  gage  pressure  and  for  the  horse-power 
given  under  Adiabatic  Compression  (Articles  46,  47  and  68  to 
72)  by  substituting  for  PI  or  Pa,  respectively,  the  atmospheric 
pressure  at  the  given  altitude.  The  latter  may  be  found  from 
Table  VI  or  calculated  from  formula  (2),  Article  4. 

Manufacturers  usually  build  special  compressors  for  high  alti- 
tudes which  are  designed  to  meet  the  demands  made  on  a  plant, 
located  at  considerable  elevation  above  sea  level. 


CHAPTER  VIII 
THE  COMPRESSED  AIR  INDICATOR  CARD 

82.  Inasmuch  as  the  work  performed  in  the  air  cylinder  of  a 
compressor  depends  on  so  many  variable  and  interdependent 
conditions,  it  can  only  be  studied  successfully  from  an  indicator 
card,  or  still  better  from  a  number  of  indicator  cards  taken  from 
the  air  cylinders  of  a  compressor  when  in  actual  service. 

It  is  assumed  that  the  reader  is  familiar  with  the  methods  of 
taking  an  indicator  card  and  of  calculating  from  it  the  mean 
pressure,  the  horse-power,  and  the  volumetric  efficiency.  There 
are  a  number  of  excellent  books  available  which  discuss  this 
subject  in  detail,  to  which  the  reader  is  referred. 

Besides  the  facts  regarding  power  consumption,  indicator  dia- 
grams also  convey  information  regarding  the  working  of  valves, 
the  volume  of  air  taken  in  and  compressed,  the  effect  of  clearance, 
the  efficiency  of  the  cooling  devices,  and  the  correct  or  incorrect 
proportioning  of  the  air  cylinders. 

Unfortunately,  indicator  cards  do  not  register  temperatures 
and  thus  offer  no  means  for  determining  directly  the  useful 
capacity  of  the  compressor,  expressed  in  number  of  pounds  of 
free  air  at  outside  temperature  compressed  and  delivered  per 
unit  of  time.  The  latter  is  the  only  correct  estimate  of  compressor 
capacity  for  the  reason  that  before  the  air  is  used  in  the  air  engine, 
it  has  assumed  outside  temperature  and  any  increase  in  volume, 
due  to  heat  which  the  air  may  have  received  before  or  during 
compression,  is  only  temporary  and  is  subsequently  lost  for 
useful  purposes. 

Therfore  an  indicator  card  which  shows  high  volumetric  effi- 
ciency is  in  itself  no  proof  of  the  ultimate  merits  of  a  compressor 
as  far  as  capacity  is  concerned. 

In  Article  53  it  was  shown  that  inlet  valves,  which  prevent 
ready  admission  of  air,  reduce  the  volumetric  efficiency.  This 
is  shown  on  the  air  card  by  the  suction  line  falling  considerably 
below  the  atmospheric  line.  On  the  other  hand,  an  air  card 
taken  from  a  compressor  with  leaky  inlet  valves  may  show  a 

64 


THE  COMPRESSED  AIR  INDICATOR  CARD  65 

large  volumetric  efficiency  due  to  the  fact  that  some  of  the 
clearance  air  escapes  through  them  into  the  atmosphere  and  the 
expansion  line  CG  (Fig.  8)  falls  sooner,  thus  increasing  the  dis- 
tance RG  without,  however,  increasing  the  useful  quantity  of  air 
compressed. 

In  the  same  manner  will  leaky  discharge  valves,  leaky  pistons 
and  inter-coolers  show  an  apparent  increase  in  volumetric  effi- 
ciency while  the  actual  quantity  of  air  delivered  is  diminished. 

Air  cards,  showing  practically  isothermal  compression  lines, 
are  frequently  the  result  of  a  leaky  piston  and  not  of  superior 
workmanship  in  the  construction  of  the  compressor.  A  leaky 
piston  will  reduce  the  compression  line  as  fully  or  more  effectually 
than  any  cooling  of  the  air  can  do,  so  that  anyone  not  familiar 
with  the  tricks  of  an  air  card  may  easily  be  misled  in  his  judgment 
of  the  merits  of  a  machine  from  the  indicator  card  alone. 

Evidence  of  a  leaky  piston  is  usually  given  by  a  card  showing 
the  admission  line  above  the  atmospheric  line  during  the  entire 
stroke. 

From  what  has  been  said,  it  is  evident  that  great  caution  must 
be  exercised  in  interpreting  an  air  card.  To  do  this  correctly,  it 
is  necessary  to  know  what  positive  information  an  air  card  will 
give  and  to  bear  in  mind  that  it  does  not  tell  the  whole  story. 

In  the  following  articles  a  few  air  cards  and  their  interpretation 
are  given  with  the  object  of  assisting  the  student  of  this  subject 
in  reading  and  interpreting  similar  cards. 

83.  Air  Card  of  a  Single-stage  Compressor. — Fig.  12  is  the 
facsimile  of  an  indicator  card  taken  from  the  air  cylinder  of  a 
single-stage  compressor.  On  this  card  the  actual  compression 
curve  AC  lies  between  the  adiabatic  curve  AB  and  the  isothermal 
curve  AD.  The  gage  pressure  of  the  air  in  pounds  per  square 
inch  at  any  point  M  of  the  stroke  is  measured  by  the  line  MN. 
The  card  shows  the  usual  performance  of  a  compressor  of  this 
type.  When  the  piston  has  reached  point  C  the  air  has  reached 
receiver  pressure  (61  Ib.  gage  on  the  card  illustrated). 

Owing  to  the  weight  of  the  discharge  valves  and  the  tension  of 
the  springs,  the  pressure  in  the  cylinder  usually  rises  a  few  pounds 
above  the  receiver  pressure  before  the  valves  open,  as  shown  at 
E.  From  this  point  to  the  end  of  the  stroke  the  pressure  drops 
to  the  receiver  pressure.  The  wavy  shape  of  the  delivery  line  is 
mainly  due  to  the  fluttering  of  the  discharge  valves. 

At  the  end  of  the  forward  stroke  at  F  the  piston  comes  to  a 


56  COMPRESSED  AIR 

standstill.  The  discharge  valves  close  and  as  soon  as  the  piston 
commences  the  return  stroke,  the  compressed  air  that  was  left 
in  the  clearance  space  begins  to  expand  until  it  reaches  atmos- 
pheric pressure  at  G.  At  this  moment  the  inlet  valves  should 
open,  but  they  are  usually  held  for  a  moment  against  their  seats 
by  the  tension  of  the  springs.  A  partial  vacuum  is  thus  created 
behind  the  receding  piston,  causing  the  expansion  line  FG  to 
drop  below  the  atmospheric  line  as  shown  at  0,  whence  it  returns 
to  the  atmospheric  line  as  soon  as  the  valves  open. 


RECEIVER    PRESSURE    61    IBS. 


-PISTON  DISPLACEMENT 

FIG.  12. 


Free  air  is  now  admitted  and  if  the  inlet  area  is  not  restricted, 
the  admission  line  will  closely  follow  the  atmospheric  line  from 
G  to  A.  A  considerable  drop  below  the  atmospheric  line  indi- 
cates that  air  is  not  admitted  as  freely  as  should  be.  This  may 
happen  when  the  slowing  down  of  the  piston  at  the  end  of  the 
stroke  permits  the  springs  to  close  the  inlet  valves  before  the 
piston  has  completed  its  stroke.  This  reduces  the  volumetric 
efficiency  of  the  compressor  to  the  volume  GR,  because  on  the 
next  forward  stroke  the  piston  must  travel  a  distance  AR  before 
the  atmospheric  line  is  reached  and  before  actual  compression 
begins. 

The  line  EG  measures  the  extra  volume  taken  up  by  the  clear- 
ance air  after  expansion.  It  represents  a  loss  which  can  be 
minimized  by  reducing  the  clearance  space  but  cannot  be  avoided 
altogether.  Theoretically,  the  loss  is  one  of  capacity  only  and 
not  of  power;  for,  although  this  air  required  work  in  compressing 


THE  COMPRESSED  AIR  INDICATOR  CARD  67 

it  to  receiver  pressure,  in  expanding  it  helps  to  compress  the  air 
on  the  other  side  of  the  piston.     (See  Article  52.) 

84.  Air  Card  of  a  Two-stage  Compressor. — Fig.  13  shows  the 
combined  cards  taken  from  the  crank-end  of  a  two-stage  com- 
pressor. 

Low-pressure  air  cylinder 32  1/2X48  in. 

High-pressure  air  cylinder 20  1/4X48  in. 

Piston  speed 480  ft.  per  minute. 

Piston  displacement  per  stroke 22. 13  cu.  ft. 

Pressure  of  inlet  air 14 . 00  Ib.  absolute. 

Discharge  pressure 78 . 00  Ib.  gage. 

Volumetric  efficiency  (from  card) 95  per  cent. 

Actual  free  air  (from  card) 2519  cu.  ft.  per  minute. 

Air  horse-power  (from  card) 416. 

The  theoretical  horse-power  required  for  single-stage  com- 
pression of  the  same  quantity  of  air  is  384,  showing  an  excess  of 
power  consumed  over  a  single-stage  compression,  amounting 
to  8.5  per  cent. 

This  card,  which  is  one  of  many  that  may  be  taken  from  other- 
wise well-built  two-stage  compressors,  shows  that  in  actual  prac- 
tice two-stage  compression  does  not  always  result  in  a  saving  of 
power  as  would  appear  from  theoretical  calculations. 

Whenever  there  is  an  overlap  of  the  indicator  cards  taken 
from  the  low-  and  high-pressure  cylinders  of  an  air  compressor, 
or  when  they  run  above  the  discharge  pressure  or  materially 
below  the  in- take  (atmospheric)  pressure,  there  "is  power  used  in 
excess  of  the  saving  due  to  inter-cooling.  Two-stage  compressors 
giving  cards  such  as  shown  in  Fig.  13  fail  to  realize  a  saving  of 
power  over  single-stage  compressors  usually  through  one  or  the 
other  of  the  following  defects. 

a.  Cylinders  not  properly  proportioned  for  the  prevailing  com- 
pression ratio.     In  the  case  illustrated,  the  high-pressure  cylinder 
seems  to  be  too  small  and  the  low-pressure  cylinder  has  to  per- 
form too  much  of  the  compression  work. 

b.  Inter-cooler  too  small  or  inefficient.     The  theoretical  sav- 
ing of  power  is  based  on  perfect  cooling  of  the  air  to  initial  tem- 
perature after  leaving  the  low-pressure  cylinder.     Failure  on  the 
part  of  the  inter-cooler  to  do  this  will  increase  the  work  in  the 
high-pressure  cylinder. 

c.  Valve  areas  too  small   and  air  passages  restricted.     Re- 


gg  COMPRESSED  AIR 

stricted  inlet  valve  area  in  low-pressure  cylinder  not  only  in- 
creases the  work  to  be  done  but  also  reduces  the  compressor 
efficiency.  Restrictions  in  the  high-pressure  inlet,  and  low- 
pressure  discharge  valve  areas,  and  in  the  inter-cooler  and  its 
piping,  produce  an  excess  in  the  discharge  pressure  from  low- 
pressure  cylinder  to  inter-cooler  and  a  depression  in  the  suction 
line  of  high-pressure  indicator  cards.  The  result  of  this  is  a 


ECEIVER    PRESSURE 


CRANK  END 

FIG.  13. — Combined  Air  Cards  of  a  Two-stage  Compressor. 

great  overlap  in  the  developed  diagrams  where  the  high-  and  low- 
pressure  cards  come  together.  These  pressure  losses  also  pro- 
duce an  unequal  distribution  of  the  work  in  the  two  cylinders. 

From  Article  60  the  terminal  pressure  in  the  low-pressure 
cylinder  should  have  been: 

Pi  =  VPaPz  =  V14^0(78+14)  =  36  Ib.  absolute. 

A  glance  at  the  diagram  shows  that  the  discharge  valves  of 
the  low-pressure  cylinder  did  not  open  until  the  pressure  has 
reached  nearly  50  Ib.  absolute,  indicating  a  large  waste  of  energy. 

85.  Fig.  14  shows  the  combined  air  cards,  taken  from  both 
the  head-end  and  crank-end  of  a  two-stage  Nordberg  com- 
pressor. A  comparison  of  these  cards  with  the  one  shown  in  Fig.  1 3 


THE  COMPRESSED  AIR  INDICATOR  CARD 


69 


8,    8,    g,    8,    S,    3,    §8,    8,    3, 


70  COMPRESSED  AIR 

reveals  far  more  perfect  conditions.  The  in-take  line  of  the  low- 
pressure  cylinder  closely  follows  the  atmospheric  line,  showing 
unrestricted  in-take  areas.  The  compression  line  of  the  high- 
pressure  cylinder  begins  at  the  intersection  of  the  isothermal 
compression  line  with  the  delivery  line  of  the  low-pressure  cylin- 
der, showing  perfect  inter-cooling;  and  the  fact  that  the  dis- 
charge line  of  the  low-pressure  cylinder  is  practically  identical 
with  the  in-take  line  of  the  high-pressure  cylinder  and  is  nearly 
a  straight  line,  shows  satisfactory  condition  of  valves  and  proper 
proportioning  of  the  cylinders  for  the  prevailing  ratio  of  com- 
pression. 

Low-pressure  air  cylinder 29X42  in. 

High-pressure  air  cylinder 19X42  in. 

Piston  speed 364  ft.  per  minute. 

Piston  displacement  per  stroke 15.84  cu.  ft. 

Pressure  of  inlet  air 14 . 7  Ib.  absolute. 

Discharge  pressure 80 . 0  gage. 

Volumetric  efficiency  (from  card) 98 . 7  per  cent. 

Actual  free  air  per  minute  (from  card) . . .  1611  cu.  ft. 

Air  horse-power  (from  card) 237 

The  theoretical  horse-power  required  for  single-stage  com- 
pression of  the  same  quantity  of  air  is  256,  showing  a  saving  of 
power  over  single-stage  compression  amounting  to  8  per  cent. 


CHAPTER  IX 

COOLING  WATER  REQUIRED  IN  COMPRESSION;  EFFICIENCY 

OF  COMPRESSOR  PLANT;  AIR-COMPRESSOR 

EXPLOSIONS 

86.  Amount  of  Cooling  Water  Required  in  Air  Compressors. 

Let  W  =  weight  of  required  water  in  pounds  per  unit  of  time. 
w  =  weight  of  air  in  pounds  to  be  cooled  per  unit  of  time. 
t  =  initial  temperature  of  free  air  in  degrees  Fahr. 

=  initial  temperature  of  cooling  water  in  degrees  Fahr. 
ti  =  final  temperature  of  compressed  air  in  degrees  Fahr. 
s  =  specific  heat  of  air. 

We  have  seen  that  the  amount  of  heat  required  to  raise  the 
temperature  of,l  Ib.  of  water  1°  Fahr.  is  1  B.T.U.  Accordingly, 
the  number  of  pounds  of  water  required  to  abstract  a  quantity 
of  heat  from  any  substance  without  raising  the  temperature  of 
the  water  more  than  1°  Fahr.  is  equal  to  the  number  of  B.T.U. 's 
to  be  abstracted. 

Now,  if  "w"  pounds  of  air  have  been  heated  during  compres- 
sion from  an  initial  temperature  t°  to  a  final  temperature  ti° 
Fahr.,  the  rise  in  temperature  is  (ti  —  t)°  Fahr. 

In  order  to  cool  this  quantity  of  air  to  initial  temperature, 
we  must  abstract  from  it  an  amount  of  heat,  which,  expressed 
in  B.T.U.'s,  is 

B.T.U.'s  =  M>(*i-Os  (1) 

This  also  represents  the  number  of  pounds  of  cooling  water 
required,  having  the  same  initial  temperature  as  the  in-take  air. 
Therefore 

W  =  w(ti-f)8  (2) 

Since  in  compressor  practice  the  air  is  cooled  under  constant 
pressure,  the  specific  heat  is  from  Article  8. 

s  =  0.2375 

Example. — How  many  gallons  of  water  per  minute  are  required  to 
cool  to  initial  temperature  800  cu.  ft.  of  free  air  per  minute,  compressed 

71 


72  COMPRESSED  AIR 

to  80  Ib.  gage?     Initial  temperature  of  water  and  free  air  to  be  60° 
Fahr.;  temperature  of  water  when  leaving  cooling  devices  to  be  not 
more  than  61°  Fahr. 
One  pound  of  water  =  0.12  gal. 

From  column  9,  Table  V,  we  find  the  final  temperature  of  air,  com- 
pressed adiabatically  in  two  stages  to  80  Ib.  gage  =  224°  Fahr.,  which 
is  an  increase  of  (224— 60)  =  164°. 

From  Table  I,  800  cu.  ft.  of  free  air  at  60°  Fahr.  weigh  800X0.0764  = 
61.12  Ib. 

Therefore  B.T.U.'s  to  be  abstracted  from  air  =  61.12X164X0.2375  = 
2380  and  water  required  per  minute  =  2380X0.12  =  290  gal. 

In  practice  it  is  usually  deemed  satisfactory  to  allow  an  increase  of 
temperature  in  the  water,  amounting  to  from  10  to  25  degrees,  thereby 
reducing  the  quantity  of  cooling  water  required.  If  the  initial  tempera- 
ture of  the  water  is  60°  Fahr.  when  entering  and  70°  Fahr.  when  leaving 
the  cooling  devices,  then  every  pound  of  water  has  absorbed  10  B.T.U.'s 
from  the  heated  air  and  the  number  of  pounds  of  water  required  in  this 

290 
case  will  be  only  one-tenth  of  the  quantity  stated  above,  that  is  -y^  =  30 

gal.  per  nr.inute  (nearly). 

In  actual  compression,  considerable  radiation  is  going  on  and  the 
final  temperature  of  the  compressed  air  is  less  than  the  theoretical  tem- 
perature taken  from  the  table.  It  is  therefore  safe  to  divide  the  theo- 
retical quantity  of  water  as  found  from  equation  (2)  by  two  or  even 
three. 

For  the  case  assumed,  the  minimum  quantity  of  cooling  water  re- 
quired would  therefore  be: 

on 

-5  =  10  gal.  per  minute. 

When  water  is  scarce  and  has  to  be  used  over  and  over  again,  it  be- 
comes necessary  to  cool  it  by  artificial  means  to  initial  temperature 
before  returning  it  to  the  cooling  devices  of  the  compressor.  The 
greater  its  temperature  when  leaving  the  compressor,  the  slower  and  the 
more  expensive  will  be  the  artificial  cooling  which  is  usually  accomplished 
in  so-called  cooling-towers.  Hence  the  practical  limit  of  permissible 
increase  in  temperature,  which  is,  as  stated  above,  from  10  to  15  degrees 
above  initial  temperature. 

EFFICIENCY  OF  A  PLANT  FOR  THE  PRODUCTION  OF 
COMPRESSED  AIR 

87.  Compressor  efficiency  is  a  term  which  is  used  rather 
loosely.  Usually  it  is  meant  to  designate  the  ratio  between 
the  theoretical  power  required  to  compress  and  deliver  a  certain 


EFFICIENCY  OF  A  COMPRESSOR  PLANT  73 

quantity  of  free  air  and  the  actual  power  expended.  This  is  the 
mechanical  efficiency  of  a  compressor,  strictly  speaking.  Volu- 
metric efficiency  is  explained  under  Article  53. 

What  is  important  to  know  in  the  end  is  the  efficiency  of  the 
complete  plant  for  the  production  of  compressed  air,  including 
the  compressor  itself  with  all  its  accessories  such  as  air  in-takes, 
inter-coolers,  after-coolers,  receivers,  and  so  forth. 

We  wish  to  know  the  power  value  of  a  certain  quantity  of 
compressed  air  after  it  has  left  the  compressor  and  has  cooled 
down  to  initial  temperature.  All  energy  expended  beyond  that 
value  is  lost  for  useful  purposes.  This  loss  is  chargeable  to  the 
installation  for  the  production  of  compressed  air  and  its  total 
amount  measures  the  lack  of  efficiency  of  the  installation. 

To  compute  the  efficiency,  we  must  take  into  account  all 
losses  that  occur  from  the  moment  the  air  is  taken  into  the 
cylinder  of  the  compressor  until  it  is  delivered  into  the  pipe  line  at 
practically  initial  temperature. 

These  losses  have  been  frequently  alluded  to  in  previous 
articles.  They  are  as  follows: 

1.  Losses  are  due  to  initial  temperature  of  the  in-take  air. 
It  has  been  pointed  out  that  under  ordinary  circumstances  air 
will,  after  compression  and  before  use,  assume  the  temperature 
of  natural  objects.  For  compressor  computations  this  is  usually 
taken  as  60°  Fahr. 

We  will  assume  that  we  wish  to  produce  a  volume  of  air  com- 
pressed to  70  Ib.  gage  which,  after  having  cooled  down  to  60° 
Fahr.,  is  the  equivalent  of  500  cu.  ft.  of  free  air  per  minute.  If  the 
in-take  air  has  a  temperature  of  60°  Fahr.,  the  amount  of  air  to  be 
compressed  is,  of  course,  500  cu.  ft.  per  minute.  To  compress 
adiabatically  in  one  stage  500  cu.  ft.  of  free  air  per  minute  to  70 
Ib.  gage,  and  deliver  it  into  the  receiver,  requires  (from  column  4, 
Table  V)  theoretically  74.00  h.p. 

If  the  temperature  of  the  in-take  air  had  been  100°  Fahr.  and 
500  cu.  ft.  of  it  were  cooled  down  under  constant  pressure  to  60 
degrees,  they  would  occupy  a  volume  of: 


500X  (60+461) 
Fl=     (100+461)"  =4 
which  is  less  than  the  required  volume. 


74  COMPRESSED  AIR 

Therefore,  in  order  to  have  in  the  end  a  volume  of  compressed 
air  which  when  cooled  to  60°  Fahr.  is  the  equivalent  of  500  cu.  ft. 
of  free  air,  we  should  have  compressed  more  than  500  cu.  ft.  of 
the  100  degree  air.  The  volume  to  be  compressed  in  this  case 
is: 

500X  (100+461) 
(60+461)  ~ 

To  compress  adiabatically  in  one  stage  538  cu.  ft.  of  free  air  per 
minute  to  70  Ib.  gage,  and  deliver  it  into  the  receiver,  requires 
(from  column  4,  Table  V)  theoretically  79.62  h.p.  This  is  an 
increase  of  7  per  cent,  in  the  required  power  due  to  an  increase 
of  40  degrees  in  the  temperature  of  the  in- take  air,  or  1  per  cent,  for 
every  6  degrees. 

This  points  to  the  advantage  of  bringing  cool  air  to  the 
machine.  Neglect  to  do  so  will  result  in  power  loss  as  pointed 
out,  which  must  be  charged  to  the  compressor  plant  as  a  whole. 

2.  Losses  are  due  to  the  in-take  air  being  heated  as  it  passes 
in  very  thin  streams  over  the  valve  surfaces  which  have  been 
heated  by  the  air  under  compression.     These  losses  are  difficult 
to  ascertain,  since  an  indicator  card  gives  no  hint  whatever  of 
their  occurrence.     Indicators  record  pressure  only,  not  tempera- 
tures.    These  losses  add  to  those  stated  under  (1),  and  may  be 
considerable. 

3.  Losses  are  due  to  imperfect  valves.     Poppet  valves  being 
operated  by  strong  springs  are  liable  to  throttle  the  inlet  air, 
the   effect   of   which   is   scarcely  noted   on   ordinary   indicator 
cards.     Nevertheless,  such  throttling  results  in  the  creation  of  a 
partial  vacuum  which  cuts  down  the  capacity  as  pointed  out 
under  Article  53  and  being  a  drag  on  the  machine  consumes  more 
power  in  addition  to  power  required  for  the  extra  number  of 
revolutions  needed  to  make  up  for  capacity  loss. 

4.  Losses  are  due  to  clearance.     They  have  been  discussed  in 
Article  52.     The  ultimate  effect  of  clearance  is  the  delivery,  into 
the  receiver,  of  a  volume  of  air  smaller  than  that  which  has 
actually  been  compressed  at  each  stroke  of  the  piston. 

5.  Losses  are  due  to  the  generation  of  heat  during  compression 
which  is  afterward   dissipated  and  completely  lost   for  useful 
work.    These  are  by  far  the  most  serious  losses  incident  to  air 
compression,   and  have  therefore  received  close  attention  by 
designers  and  builders  of  air  compressors.     All  attempts  have 


EFFICIENCY  OF  A  COMPRESSOR  PLANT  75 

been  directed  toward  the  accomplishment  of  isothermal  com- 
pression by  the  introduction  of  water-jackets  and  of  inter-coolers 
in  stage  compressors.  At  the  present  state  of  the  art,  these 
losses  are  unavoidable.  But  by  judicious  selection  of  com- 
pressors provided  with  adequate  cooling  devices  they  can  be 
reduced  to  a  minimum. 

6.  Losses  are  due  to  imperfect  design,  carelessness  in  handling, 
neglect  in  properly  lubricating,  stopping  leaks,  and  removing 
worn-out  parts  of  the  compressor. 

Example.  —  Let  the  piston  displacement  of  the  air  cylinders  of  a  single- 
stage  compressor  be  10  cu.  ft.  and  the  temperature  of  the  free  air  taken 
into  this  cylinder  be  60°  Fahr.  In  passing  over  the  heated  inlet  valves 
and  coming  in  contact  with  the  heated  cylinder  walls,  its  temperature 
will  rise,  let  us  say,  to  70°  Fahr.  We  have  no  means  at  present  to 
measure  this  accurately.  The  theoretical  power  required  to  compress 
in  one  stage  adiabatically  10  cu.  ft.  of  free  air  to  70  Ib.  gage  and  deliver 
it  into  the  receiver  is: 


To  this  we  will  add  15  per  cent,  for  friction  etc.,  which  gives 

Wn  =  55,600  ft.-lb.  (1) 

Neglecting  jacket  cooling  and  radiation,  the  temperature  of  the  com- 
pressed air  will  be: 

n_-_l 

T,  =  T(P^  n  =  (70+461)  x(^y)°'29  =  882  degrees  absolute. 
The  volume  V2  into  which  the  air  has  been  compressed  will  be: 


^J       -  2.88  cu.  ft. 

If  the  clearance  of  the  compressor  is  2  per  cent.,  the  actual  volume  of 
compressed  air  delivered  into  the  receiver  is  not  72  but: 

73  =  2.88- }?. X2  =  2.68  cu.  ft. 

1UU 

It  is  true  that  the  expanding  clearance  air  helps  to  compress  air  on  the 
return  stroke  of  the  piston,  that  is,  the  value  of  Wn  as  stated  in  equa- 


76  COMPRESSED  AIR 

tion  (1)  will  be  somewhat  less.  On  the  other  hand,  this  clearance  air 
having  a  temperature  of  882  degrees  absolute,  in  mingling  with  the  in- 
coming free  air  will  raise  its  temperature  somewhat  beyond  that  which 
we  have  allowed  for  heating  during  contact  with  the  heated  inlet 
valves,  so,  for  the  sake  of  demonstration  we  shall  neglect  the  gain  in 
required  power  for  compression. 

Now,  the  pressure  of  this  volume  V3  of  air,  having  a  temperature  of 
882  degrees  absolute,  in  cooling  down  to  a  temperature  of  60°  Fahr. 
under  constant  volume,  will  decrease  to  a  pressure  P3  which  we  deduce 
irom  formula  in  Article  19: 


P3=(70+14.7)    ~t  .         =  50  Ib.  absolute. 

\      58Z      / 

We  have  then  in  the  end  a  volume  of  2.68  cu.  ft.  of  air  at  an  absolute 
pressure  of  50  Ib.  and  a  temperature  of  60°  Fahr.,  which,  if  allowed  to 
expand  adiabatically  to  initial  pressure  (14.7  Ib.  absolute)  is  theoreti- 
cally capable  of  performing  an  amount  of  work,  which  we  deduce  from 
formula  (1),  Article  110. 


144Xl.406X50x2.68f,      /14.7\029~| 

0.406  I1'  Uo)      J=  20,000  ft.-lb. 

This  is  the  power  value  of  the  compressed  air  which  we  started 
out  to  determine. 

The  efficiency  of  our  compressor  plant,  that  is,  of  the  complete 
installation  for  the  production  of  compressed  air  is  in  the  case 
under  consideration: 

20,000 

=  0.36  =  36  per  cent. 


Under  favorable  conditions  the  actual  efficiency  may  be  greater, 
due  to  the  fact  that  the  final  temperature  of  the  compressed  air 
will  be  less  than  882  degrees  absolute  because  of  jacket  cooling 
and  radiation.  In  many  plants  the  efficiency  is  considerably  less. 

For  stage  compressors  the  theoretical  efficiency  is  higher  than 
for  single-stage  compressors,  because  the  work  of  compression 
and  delivery  is  less.  But  a  stage  compressor  is  a  more  ex- 
pensive machine  and  only  warranted  when  the  reduction  in 


AIR-COMPRESSOR  EXPLOSIONS  77 

operating  costs  more  than  compensates  for  the  original  invest- 
ment. 

Practical  stage-compressor  tests  frequently  show  an  excess 
of  power  consumed,  rather  than  a  saving  over  single-stage 
compression.  (See  Chapter  VIII  on  Indicator  Cards.) 

AIR-COMPRESSOR  EXPLOSIONS 

88.  In  general,  an  explosion  is  due  to  quick  combustion,  fol- 
lowed by  the  generation  of  a  large  volume  of  gas,  which,  if  con- 
fined, suddenly  increases  the  pressure  against  the  enclosing  walls 
beyond  their  strength  of  resistance. 

If  an  explosion  occurs  in  an  air  compressor,  we  must  trace  the 
cause  to  the  presence  in  the  air  cylinder  of : 

1.  A  combustible  substance  in  a  finely  divided  state  so  as  to 
permit  practically  instantaneous  ignition  of  the  whole  mass  and 
therefore  the  sudden  generation  of  a  large  volume  of  gas. 

2.  Of  air  or  oxygen  in  the  proper  proportion  to  completely 
oxidize  the  combustible,  so  as  to  form  an  explosive  mixture. 

3.  A  temperature  high  enough  to  ignite  the  mixture. 

The  absence  of  any  one  of  the  above  three  conditions  will 
make  an  explosion  impossible.  This  points  to  the  preventive 
measures  enumerated  below. 

1.  Combustibles:  The  only  combustible  substance  purposely 
introduced  into  the  air  cylinder  of  a  compressor  is  the  lubricat- 
ing oil.  Incidentally,  whatever  combustible  substance  may  be 
contained  in  the  atmosphere  will  be  drawn  into  the  cylinder 
during  the  suction  stroke.  If  consisting  of  fine  coal  dust,  for 
instance,  the  danger  of  an  explosion  will  be  materially  increased. 

One  of  the  ingredients  of  a  lubricating  oil  is  carbon,  which 
will  separate  out  from  the  oil  under  the  influence  of  heat  and 
pressure  and,  if  permitted,  will  eventually  accumulate  in  such 
quantities  as  to  make  an  explosive  mixture  with  the  air. 

The  requirement  that  the  combustible  must  be  finely  divided 
is  satisfied  by  the  vapors  of  the  oil,  given  off  under  high  tempera- 
tures. When  it  is  considered,  however,  that  the  vapors  thus 
formed  are  expelled  from  the  air  cylinder  with  each  stroke, 
only  the  most  reckless  use  of  lubricating  oil  would  furnish  enough 
vapors  during  one  stroke  of  the  piston  to  form  an  explosive 
mixture  with  the  air.  Thus  it  becomes  highly  improbable  that 
the  presence  of  such  vapors  alone  ever  causes  an  explosion.  It 


78  COMPRESSED  AIR 

is  nevertheless  possible  that  in  an  air  cylinder  with  leaky  valves 
and  piston,  enough  of  these  vapors  may  eventually  accumulate 
to  at  least  assist  in  an  explosion. 

It  is  more  probable  that  carbonaceous  matter  in  a  finely  divided 
or  porous  state  is  the  chief  cause  of  an  explosion,  when  present 
in  the  proper  proportion  and  exposed  to  abnormal  temperatures. 

2.  The  proportion  of  combustible  matter  and  air  or  oxygen, 
required  to  form  an  explosive  mixture,  is  dependent  on  the  nature 
of  the  combustible.     We  are  fairly  well  acquainted  with  these 
proportions  when  the  mixture  takes  place  under  atmospheric 
pressure.     What  they  are  under  the  high  pressures  prevailing 
in  the  cylinder  of  an  air  compressor  is  a  question  which  can  only 
be  answered  when  more  reliable  data  become  available. 

3.  The  temperature  required  to  ignite  an  explosive  mixture 
under  atmospheric  pressure  we  also   know  fairly  well.     Finely 
divided  carbon,  for  instance,  ignites  at  a  temperature  of  600° 
Fahr.     Under  high  pressure,  it  is  quite  possible  that  ignition 
takes  place  at  a  temperature  considerably  below  that. 

However  conducive  oil  may  be  to  an  explosion,  its  use  as  a 
lubricant,  and  therefore  the  accumulation  of  carbonaceous  matter 
and  the  formation  of  vapors,  cannot  be  avoided  altogether. 
But  by  proper  care  and  perfect  cooling  devices,  the  temperature 
can  be  kept  within  safe  limits.  To  do  this,  we  must  know  the 
conditions  which  cause  abnormal  temperatures.  Chief  among 
them  are  the  following: 

o.  When  air  is  taken  into  the  cylinder  from  a  hot  engine  room 
or  from  the  neighborhood  of  a  boiler  room.  Other  evil  effects 
of  such  conditions  have  already  been  pointed  out  under  Article  87. 

Air  at  a  temperature  of  150°  Fahr.  and  compressed  in  one  stage 
to,  say,  75  Ib.  gage,  would  have  a  final  temperature  of 


0-29 


Tl=s  T(9Yn  =  (150+461)  ( 75+1?4-7-)  =1030° absolute 

=  569°  Fahr. 

which  even  if  reduced  somewhat  by  water-cooling  would  come 
dangerously  close  to  or  exceed  the  ignition  point  of  any  explosive 
substance. 

6.  When  the  maximum  pressure  for  which  the  compressor  is 
built  is  willfully  or  accidentally  exceeded.  The  final  temperature 
is  thus  raised  to  a  point  beyond  the  efficiency  of  the  cooling  ap- 


AIR-COMPRESSOR  EXPLOSIONS  79 

pliances  and  will  ultimately  reach  the  ignition  point  of  an  ex- 
plosive mixture. 

c.  When  the  pressure  is  exceeded  by  reason  of  a  gradual  ac- 
cumulation of  carbonaceous  matter  of  the  oil  in  the  discharge 
valves.     This  contracts  the  passage  and  requires  higher  pressure 
for  the  delivery  of  a  certain  amount  of  air  in  a  given  time,  thus 
raising  the  temperature. 

d.  When  valves  are  not  kept  clean  and  pistons  are  permitted 
to  wear  loose,  which  causes  leakage  of  compressed  air  into  the 
in-take  side  of  the  cylinder.     This  is  probably  the  most  frequent 
source  of  excessive  temperature.     The  leakage  air  expands  to 
atmospheric  pressure  without  doing  work,  hence  loses  none  of 
its  heat  (see  Article  118),  and  in  mixing  with  the  incoming  free 
air  it  raises  the  temperature  of  the  mixture  which  is  to  be  com- 
pressed on  the  following  stroke  to  a  dangerous  degree. 

The  dangerous  effect  of  leakage  in  the  air  cylinders  of  a  com- 
pressor is  shown  in  the  following  example: 

Example. — Let  W0  =  weight  of  a  given  quantity  of  atmospheric  air, 
occupying  a  volume  equal  to  the  piston 
displacement. 

=  unity  (assumed)  =  1  =  Wi+ Wz- 
Wi  =  weight  of  atmospheric  air  which  enters  the 
cylinders  at  each  stroke  at  an  absolute  tem- 
perature T\. 
=  l-W2. 

Wz  =  weight  of  leakage  air,  having  an  absolute  tem- 
perature Tz  and  which  expands  to  atmospheric 
pressure  upon  entering  the  in-take  side  of  the 
cylinder. 
P0  =  absolute  pressure  of  atmospheric  air  in  pounds 

per  square  inch. 
Pz  =  absolute  pressure  of  compressed  air  in  pounds 

per  square  inch. 
c  =  specific  heat  of  air. 
n  =  1.406. 


It  is  evident  that  the  total  quantity  of  heat  in  the  mixture  W0  must 
be  equal  to  the  sum  of  the  heat  quantities  contained  respectively  in 
Wi  and  in  Wz  before  mixing.  If  the  absolute  temperature  of  W0  has 
become  T0  after  the  mixing  of  the  leakage  with  the  atmospheric  air, 
then: 


80  COMPRESSED  AIR 

Total  heat  in  W0  =  WuT0c 
Total  heat  in  W i  =  TFiTV 
Total  heat  in  W2  =  W2T2c 
and  W0T0c  =  c(WiTi+ W2T2) 

Remembering  that         W0  =  1  and  Wi  =  1  -  Tf2 

We  find  T0  =  T1(l-W2)  +  T2W2  (I) 

If  the  temperature  before  compression  is  T0,  then  the  temperature  T2 
after  compression  to  an  absolute  pressure  P2  according  to  equation  (11), 
Article  41,  is: 


T,  =  T0y  (2) 

Let  the  temperature  of  the  in-take  air  be  60°  Fahr. 
then  TI  =  60+461  =  521  degrees  absolute. 

Let  leakage  air  equal  15  per  cent,  of  W0 

then  W2=10"0X15  =  I50X  15  =  0'15 

Let  the  air  be  compressed  to  85  Ib.  gage, 
then  P2  =  85+ 14.7  =  99.7 

If  we  assume  the  compressor  to  have  made  a  number  of  strokes 
before  leakage  occurs,  then  the  temperature  of  the  compressed  air  will 
be  447°  Fahr.  (Col.  8,  Table  III).  If  leakage  now  begins  at  a  rate  of 
15  per  cent,  we  have  T0  from  equation  (1): 

T0  =  (60+461) (1-0.15)  +0.15(447+461)  =  579  degrees  absolute. 
If  we  compress  this  air  to  85  Ib.  gage,  its  final  temperature  will  be  from 
equation  (2): 

T2  =  579 X6.782°'29  =  1005  degrees  absolute  =  544°  Fahr. 

Some  of  this  compressed  air  leaks  into  the  in-take  side  of  the  cylinder 
where  we  get  an  air  mixture  of  the  temperature: 

T0  =  (60-H61)(1-0.15)+0.15(544-H61)  =  595  degrees  absolute 
and  this  air  compressed  to  85  Ib.  gage  will  have  a  temperature 
T*  =  595  X  6.782°- 29  =  1037  degrees  absolute  =  576°  Fahr.,  etc. 

This  shows  that  the  temperature  in  the  cylinder  is  increasing  with 
every  stroke  of  the  piston  and  in  spite  of  the  cooling  devices  will  soon 
reach  a  point  at  which  in  the  presence  of  combustible  material  and  in- 
flammable vapors  an  explosion  is  likely  to  occur. 

The  danger  increases  when  the  compressor  is  running  at  slow  speed. 
Leakage  is  a  constant  quantity  per  unit  of  time.  Hence  in  a  slow-speed 
machine  the  percentage  of  leakage  air  per  stroke  will  increase  and  that 
of  the  cool  in-take  air  will  decrease.  As  a  consequence  the  tempera- 
ture of  the  mixture  to  be  compressed  on  the  next  stroke  will  be  propor- 
tionally higher,  thereby  increasing  the  danger  of  an  explosion. 


AIR-COMPRESSOR  EXPLOSIONS  81 

89.  Compressors,  using  throttling  devices  for  the  regulation 
of  intermittent  demand,  may  under  certain  conditions  develop 
dangerous  temperatures.     By  throttling  the  inlet,   the  initial 
pressure  is  lowered,  while  the  ratio  of  compression  is  increased. 
As  a  result,  the  final  temperature  will  be  considerably  higher 
than  under  normal  conditions,  so  high  as  to  ignite  any  explosive 
substance  that  may  be  present  in  the  cylinder. 

Example. — Let  us  assume  that  the  output  of  a  single-stage  compressor, 
working  against  60  Ib.  pressure  is  to  be  reduced  by  throttling  to  one- 
fourth  of  its  full  capacity.  If  atmospheric  pressure  is  14.7  Ib.  per  square 
inch,  the  pressure  of  the  in-take  air  will  become: 

14.7 

— r — =  o.7  ID.  per  square  men, 

and  the  total  ratio  of  compression: 

Pl     60+14.7 
P~      3.7 

If  the  initial  temperature  of  the  air  is  70°  Fahr.,  the  final  temperature, 
from  equation  (11),  Article  41,  will  be: 

n-l 

\  n   -(70+461)  20.2  °'!9  =  1270 degrees  absolute, 309° Fahr. 

Although  radiation  and  jacket-cooling  will  considerably  reduce  this 
temperature,  the  figures  nevertheless  indicate  the  danger  connected 
with  compression  of  rarefied  air  such  as  obtains  in  compressors  regulat- 
ing the  output  by  throttling  the  in-take. 

90.  Prevention  of  Compressor  Explosions.^ — Having  pointed 
out  the  most  likely  causes  of  an  explosion  in  a  compressor,  the 
means  of  prevention  become  self-evident.     They  consist  first  in 
guarding  against  accumulation  of  explosive  substances  in  the 
air  cylinder,  and  second  in  keeping  down  temperatures  below 
the  danger  point. 

The  first  is  accomplished  by  using  a  lubricant  which  does  not 
precipitate  its  carbon  contents  at  normal  temperatures  and  by 
using  it  sparingly.  Soapy  water  fed  at  intervals  to  the  cylinder 
is  good  practice.  Inspect  the  valves  frequently  and  remove  all 
accumulations  of  foreign  substances. 

Abnormal  temperatures  are  prevented  by  water-jacketing 
and  inter-coolers,  if  they  are  of  proper  design  and  magnitude. 
Leaks  in  valves  and  piston,  as  pointed  out,  prevent  the  most 
perfect  cooling  devices  from  doing  their  duty.  They  should  be 
stopped  as  soon  as  discovered. 


PART  II 

THE  TRANSMISSION  OF  COMPRESSED  AIR 


CHAPTER  X 
TRANSMISSION  OF  COMPRESSED  AIR 

91.  Compressed  air,  before  being  used  in  so-called  air  engines, 
has  to  be  conveyed  from  the  compressor  room  to  the  points  of 
use  in  iron  pipes  of  various  dimensions.     The  question  then  arises : 
What  should  be  these  dimensions  so  as  to  satisfy  the  demand  for 
compressed  air  at  the  discharge  end  of  the  pipe  line? 

The  solution  of  this  problem  requires,  besides  a  knowledge  of 
the  behavior  of  compressed  air  flowing  through  a  pipe  line,  a 
careful  study  of  local  conditions  and  a  close  comparison  of  first 
cost  of  installation  with  the  ultimate  operating  expenses. 

92.  The  laws  governing  the  flow  of  compressed  air  in  iron 
pipes  are  far  more  elusive  and  complex  than  those  for  water, 
owing  to  the  fact  that  compressed  air  is  not  a  stable  substance 
like  water  but  changes  its  pressure,  density,  volume,  velocity  and 

'friction  at  every  point  of  the  pipe  line. 

Attempts  to  express  these  laws  in  simple  formulas,  which 
would  hold  good  in  all  cases,  seem  therefore  quite  hopeless. 
The  best  that  can  be  said  of  any  of  the  formulas  employed 
by  engineers,  is  that  the  numerical  results  obtained  from  them 
will  in  most  cases  correspond  only  approximately  with  those 
obtained  from  actual  practice.  They  must  therefore  be  used 
with  a  great  amount  of  caution. 

Before  referring  to  these  formulas,  it  is  well  to  study  the 
behavior  of  compressed  air  during  its  passage  through  a  pipe  line. 
We  have  seen  that  in  order  to  cause  air  to  flow  from  one  point  to 
another,  there  must  be  a  difference  of  pressure  in  the  air  at  those 
two  points.  That  is,  if  we  need  air  at  a  pressure  of  80  Ib.  at  a 
certain  distance  from  the  compressor,  the  pressure  of  the  air  as 
it  leaves  the  compressor  or  receiver  must  be  greater  than  80  Ib. 

This  difference  of  pressure  which  is  necessary  to  make  the  air 
flow,  represents  energy  which  does  useful  work,  that  is,  it  conveys 
the  air  from  one  place  to  another.  It  is  therefore  not  a  loss  in 
the  true  meaning  of  the  word.  But  air  in  its  passage  through  pipes 
is  subject  to  friction.  To  overcome  this  friction,  energy  in  the 

85 


86  COMPRESSED  AIR 

form  of  pressure  is  required,  additional  to  that  needed  for  keeping 
the  air  in  motion.  To  produce  this  extra  pressure  in  the  air, 
power  is  consumed  in  the  compressor  which  is  an  actual  loss  as 
there  can  be  no  useful  return  for  it. 

Friction  reduces  the  pressure  of  the  air,  and  since  the  tempera- 
ture in  the  pipe  can  be  assumed  to  be  constant,  this  reduction  of 
pressure  increases  the  volume  of  the  air.  To  force  an  increased 
volume  of  air  through  a  pipe  of  the  same  diameter  during  the 
same  time  means  increased  velocity  and  this  in  its  turn  requires 
an  additional  power  in  the  form  of  pressure. 

In  general,  the  transmission  of  air  in  pipes  entails  both  a  loss 
of  pressure  and  a  loss  of  power. 

93.  Loss  of  pressure  or  head  is  the  difference  of  pressure  in  the 
air  between  the  in-take  and  the  discharge  end  of  the  pipe  line. 
This  loss  as  has  been  mentioned  is  due : 

1.  To  pressure  consumed  in  causing  the  air  to  flow  from  one 
end  of  the  pipe  line  to  the  other.     It  is  as  explained,  not  a  loss, 
strictly  speaking. 

2.  To  pressure  consumed  in  overcoming  friction  and  increasing 
the  velocity.     This  loss  is  unavoidable  but  can  be  minimized  by 
intelligent  design  of  the  pipe  line. 

3.  To  leakage  which  causes  the  air  remaining  in  the  pipe  to 
expand  and  therefore  lose  pressure.     This  loss  is  avoidable  and 
in  a  well-constructed  pipe  line  should  be  practically  nil. 

4.  To  difference  in  elevation  between  the  compressor  room  and 
the  points  of  use.     (See  Article  97.) 

94.  Loss  of  Power. — The  ultimate  loss  of  power  which  is 
chargeable  to  transmission,  is  the  difference  between  the  amount 
of  power,  residing  in  the  compressed  air  when  it  enters  the  pipe 
line  and  that  which  is  available  at  the  discharge  end  of  the  pipe 
line.     (See  also  Articles  97  and  102.) 

Since  the  amount  of  work  required  to  compress  air  and  the 
amount  of  work  which  compressed  air  is  capable  of  performing, 
depends  on  pressure  as  well  as  on  volume  and  since  loss  of  pres- 
sure increases  the  volume  (the  temperature  remaining  the  same), 
it  follows  that  the  loss  of  power  is  not  in  direct  proportion  to  the 
decrease  in  pressure  but  is  partly  compensated  by  the  resultant 
increase  in  volume. 

For  instance,  if  air  enters  a  pipe  at  100  Ib.  and  is  discharged 
at  80  Ib.  gage,  there  is  a  loss  in  pressure  of  20  per  cent.  From 
equation  (1),  Article  110  the  theoretical  work  which  1  cu.  ft.  of 


TRANSMISSION  OF  COMPRESSED  AIR  87 

compressed  air  is  capable  of  performing  in  expanding  adiabatic- 
ally  from  100  Ib.  gage  to  atmospheric  pressure  is  25,740  ft.-lb. 
This  represents  the  potential  energy  of  1  cu.  ft.  of  air  when  it 
enters  the  pipe  line  at  100  Ib.  gage.  This  cubic  foot  of  com- 
pressed air  when  its  pressure  is  reduced  to  80  Ib.  at  the  end  of  the 
pipe  line  has  expanded  into  a  volume  of  1.211  cu.  ft.,  which  at  a 
pressure  of  80  Ib.  is  capable  of  doing  work  to  the  amount  of 
24,000  ft.-lb.  Hence  the  loss  of  power  in  this  case  amounts  to 
only  7  per  cent,  as  against  a  pressure  loss  of  20  per  cent. 

Loss  of  pressure  in  air  transmission  must  therefore  not  be  con- 
founded with  loss  of  power.  Both  losses  in  a  well-proportioned 
pipe  line  are  usually  small  compared  with  other  losses  in  the 
production  and  use  of  compressed  air,  such  as  result,  for  instance, 
from  the  heat  produced  during  compression  which  is  subsequently 
lost  in  transmission. 


CHAPTER  XI 

DIMENSIONS  OF  PIPE-LINES  FOR  CONVEYING  COMPRESSED 
AIR 

95.  From  what  has  been  said,  it  is  evident  that  no  uniform 
rule  can  be  followed  in  deciding  on  the  proper  dimensions  of 
pipes  for  air  transmission.  Almost  any  degree  of  transmission 
efficiency  can  be  obtained  by  using  pipes  of  large  diameter.  This, 
however,  may  result  in  extravagant  first  cost.  On  the  other  hand, 
an  unwise  economy  in  first  expenditure  may  reduce  the  efficiency 
of  the  whole  system  to  a  point  where  the  cost  of  operation  will 
more  than  offset  the  original  saving  in  cost  of  installation. 

A  proper  design  of  pipe  line  must  therefore  take  into  considera- 
tion not  only  first  cost  of  pipe  and  interest  thereon  but  also  the 
subsequent  operating  costs.  The  latter  will  vary  with  the  size 
of  the  compressor,  the  pipe  line,  and  with  local  conditions  such 
as  cost  of  transportation,  fuel,  labor,  etc.,  in  the  part  of  the  country 
where  the  plant  is  to  be  erected.  The  problem  must  be  solved 
for  each  individual  installation. 

In  order  to  make  comparisons,  however,  we  must  have  means 
of  calculating,  at  least  approximately,  the  minimum  dimensions 
of  a  pipe  which  will  fill  the  requirements  of  a  certain  installation. 
Or,  if  the  size  of  the  pipe  is  given,  we  must  be  able  to  calculate 
the  work  which  the  compressor  must  perform  in  order  that  the 
available  power  at  the  discharge  end  of  the  pipe  line  will  be  a 
certain  quantity.  Or,  if  a  certain  compressor  and  pipe  line  are 
on  hand,  we  must  be  able  to  calculate  the  power  that  will  be 
available  at  the  discharge  end  of  the  pipe  line  before  we  buy  and 
install  our  air  engines. 

The  conditions  that  affect  pressure,  volume,  density,  tem- 
perature, velocity  and  friction  of  the  air  passing  through  a  pipe 
line,  are  so  numerous  that  the  formulas  proposed  by  authorities 
cannot  be  expected  to  give  more  than  safe  approximate  results 
for  pipe  1'ne  dimensions.  Such  results  should  be  considered 
the  maxima  or  minima  in  each  case  and  ample  allowances  should 
be  made  for  undetermined  contingencies. 

The  formulas  selected  for  this  treatise  are  those  proposed  by 
Johnson-Rix. 


PIPE-LINES  FOR  CONVEYING  COMPRESSED  AIR          89 

96.  Formulas  for  Pipe  Line  Computations.  — 

Let  PI  and  P2  =  absolute  pressures  at  intake  and  discharge 
terminals  of  pipe,  in  pounds  per  square 
inch. 

V  =  volume  of  free-air  equivalent  in  cubic 
feet  per  minute,  passing  through  pipe. 

L  =  length  of  pipe  line  in  feet. 

D  =  diameter  of  pipe  in  inches. 


Then 


2000(P!2-P22) 

F=^^W^vj  (3) 

L_2000J)5(P12-P22) 


Pl~^2000^+P22  (5) 


T/2T 
r>  /P    2  K     -*-'  ,r>\ 

P«"\Pl  ~2000^ 

Example  1.  —  What  should  be  the  diameter  of  a  pipe  line,  1200  ft. 
long  that  will  transmit  the  equivalent  of  4000  cu.  ft.  of  free  air  per 
minute  with  a  pressure  loss  of  not  more  than  8  Ib.  Initial  pressure  = 
100  Ib.  gage.  Atmospheric  pressure  =  14.7  Ib. 


TT  ™        /^     I          40002X1200 

From  equation  (2)       D  =  \20o0(114.7*- 106.7') 

whence  D  =  5.58,  say  6  in. 

Example  2. — What  is  the  free  air  equivalent  in  cu.  ft.  per  minute  that 
can  be  transmitted  through  an  8-in.  pipe  line  11,000  ft.  long  so  that 
the  pressure  loss  is  not  more  than  5  Ib.  Initial  pressure  =  80  Ib. 
gage.  Atmospheric  pressure  at  locality  selected  =  12.02  Ib. 


„  .       ,a.        T7        /2000  X  85(92.022-  87.022) 

From  equation  (3)        I  =  "\J —        — ITOOO —    — ~ 

whence  V  =  230Q  cu.  ft.  of  free  air  per  min. 

Example  3. — What  must  be  the  initial  pressure  of  an  equivalent 
of  500  cu.  ft.  of  free  air  per  minute  so  that  at  the  end  of  a  2-in.  pipe  line, 


90  COMPRESSED  AIR 

300  ft.  long  it  has  a  pressure  of  80  Ib.  gage.     Atmospheric  pressure  at 
locality  selected  =  11.30  Ib. 

From  equation  (5)      Pi 

whence  Pi  =  97.5  Ib.  absolute 
=  86.2  Ib.  gage 

Example  4. — What  will  be  the  terminal  pressure  of  an  equivalent 
of  500  cu.  ft.  of  free  ah-  per  minute  at  the  discharge  end  of  a  5-in.  pipe 
line,  2500  ft.  long,  when  initial  pressure  =  90  Ib.  gage.  Atmospheric 
pressure  at  locality  selected  =  12.02  Ib. 


500  2X  2500 


whence  P2=  101.02  Ib.  absolute 
=  89lb.  gage 

Example  6.  —  What  is  the  permissible  length  of  a  6-in.  pipe  line  that 
will  transmit  the  equivalent  of  2000  cu.  ft.  of  free  air  per  minute  with  a 
pressure  loss  of  not  more  than  10  Ib.  Initial  pressure  =  90  Ib.  gage. 
Atmospheric  pressure  =  14.7  Ib. 

2000X65(104.72-94.72) 
From  equation  (4)        L=  200Q2  — 

whence  L  =  7750  ft. 

97.  Effect  of  Altitude  on  the  Transmission  of  Compressed 
Air.  —  The  formulas  given  under  Article  96  do  not  take  into 
consideration  any  difference  of  elevation  between  the  in-take  and 
the  discharge  end  of  the  pipe  line,  but  assume  that  the  two  ter- 
minals of  the  pipe  line  are  practically  at  the  same  elevation.  In 
compressed-air  installation,  it  happens  frequently  that  the  engines 
using  the  compressed  air  are  located  at  a  considerable  elevation 
above  the  compressor  in  which  case  proper  allowance  must  be 
made  for  the  loss  of  pressure  due  to  this  fact. 

Example.—  At  a  mine  located  1500  ft.  above  the  compressor  house, 
a  free  air  equivalent  of  4000  cu.  ft.  per  minute  is  required  at  a  gage 
pressure  of  80  Ib.  The  length  of  the  pipe  line  is  2600  ft.  Elevation  at 
compressor  is  3000  ft.  above  sea  level. 

(a)  If  a  loss  of  6  Ib.  is  allowed  for  pipe  friction,  what  must  be  the  gage 
pressure  of  the  air  when  leaving  the  compressor? 

(6)  What  should  be  the  diameter  of  the  pipe? 


PIPE-LINES  FOR  CONVEYING  COMPRESSED  AIR          91 

Solution  (a)  From  Table  VI  atmosph.  press,  at  compressor  =  13.16  Ib. 
From  equation  (4),  Art.  4,  atmosph.  press,  at  mine 

1500 
logP450o  =  log  13.16-(assuming  temp.  =  60°F.) 


Whence          P45oo  =  12.32  Ib. 

Hence,  absolute  pressure  of  compressed  air  at  mine 
P2  =  80  +12.32  =  92.32  Ib.  abs.  at  discharge  terminal  of  pipe  line. 
The  corresponding  pressure  at  the  intake  of  the  pipe  is  found  from  the 


same  formula  : 

1500 


log  Pi1  =  log  92.32+: 


122.4(60+461) 
Whence  PS  =  98.65  Ib.  absolute. 

Adding  to  this  the  6  Ib.  allowed  for  pipe  friction,  it  follows  that  the 
compressed  air  leaving  the  compressor  must  have  a  pressure  of 

P2=  104.65  abs.  or  104.65-13.16  =  91.49  Ib.  gage 

in  order  that  the  pressure  at  the  mine  may  be  80  Ib.  gage.  Obviously 
on  account  of  difference  in  altitude  alone,  an  extra  pressure  of  98.65  — 
92.32  =  6.33  Ib.  is  required. 

Solution   (b).     Introducing  the  respective  values  in  equation   (2), 
Art.  96,  we  get  diameter  of  pipe 


40002X2600 


'2000(104.652-98.652) 
Whence  D  =  6in. 

98.  Dimensions  of  Branch  Pipes. — In  selecting  the  dimensions 
for  branch  pipes  to  carry  compressed  air,  it  must  be  borne  in 
mind  that  the  carrying  capacity  of  a  pipe  is  not  directly  pro- 
portional to  the  cross-section  of  the  pipe.  Under  the  same  con- 
ditions of  length  and  head  a  3-in.  pipe,  for  instance,  will  carry 
only  16  per  cent,  of  the  volume  which  a  6-in.  pipe  can  carry. 
Therefore  if  a  6-in.  main  is  to  be  divided  into  two  branches,  two 
3-in.  pipes  would  not  do  the  work,  neither  would  the  combined 
capacities  of  a  4-  and  5-in.  pipe  be  sufficient.  This  will  be  seen 
from  Table  IX. 

Going  to  the  column  showing  the  capacities  for  a  6-in.  pipe 
and  following  this  column  down  to  the  figure  opposite  4  in.,  we 
find  that  the  capacity  of  a  4-in.  pipe  is  only  35  per  cent,  of  the 
capacity  of  a  6-in.  pipe  and  for  the  5-in.  pipe  we  find  it  to  be 
63  per  cent,  of  the  6-in.  pipe  capacity.  The  sum  of  the  4-  and  5- 
in.  pipe  capacities  is  therefore  only  98  per  cent,  of  the  6-in.  pipe 
capacity,  resulting  in  a  slight  additional  friction  from  the  point 


92  COMPRESSED  AIR 

of  diversion  of  the  branches.  If  the  branches  were  made  of  4  1/2- 
and  5-in.  pipes,  the  percentages  would  be  47  and  63  respectively, 
their  sum  110  per  cent.,  resulting  in  a  slight  decrease  of  friction 
and  therefore  an  easier  flow  beyond  the  diversion  of  the  branches. 

99.  Effects  of  Elbows  and  Bends  on  the  Flow  of  Air  in 
Pipes. — Bends  and  elbows  in  a  pipe  line  have  the  effect  of  in- 
creasing the  friction  of  the  air  and  thus  reduce  the  pressure. 
In  table  below  which  is  taken  from  the  Trade  Catalogue  of  the 
Norwalk  Iron  Works  Co.,  is  given  the  length  of  pipe  in  terms  of 
diameters  which  will  produce  the  same  frictional  effect  as  an 
elbow  having  a  certain  radius. 

For  instance,  the  frictional  resistance  in  a  6-in.  pipe  line  500 
ft.  long  containing  five  elbows  with  a  radius  of  18  in.  or  three 
diameters  each,  would  be  the  same  as  that  produced  by  a  straight 

C  y  o  04  \x  A 

pipe  line  500+-  ^j^     =  520  ft.  long. 

From  the  table  the  beneficial  effect  of  a  gradual  curve  in 
comparison  with  a  short  sharp  turn,  is  quite  evident. 

Radius  of  elbow  5         diameters.     Equivalent  length  of  straight  pipe 

7.85  diameters. 
Radius  of  elbow  3         diameters.     Equivalent  length  of  straight  pipe 

8.24  diameters. 
Radius  of  elbow  2         diameters.     Equivalent  length  of  straight  pipe 

9.03  diameters. 
Radius  of  elbow  1  1/2  diameters.     Equivalent  length  of  straight  pipe 

10.36  diameters. 
Radius  of  elbow  1  1/4  diameters.     Equivalent  length  of  straight  pipe 

12.72  diameters. 
Radius  of  elbow  1         diameter.     Equivalent  length  of  straight  pipe 

17.51  diameters. 
Radius  of  elbow     3/4  diameter.     Equivalent  length  of  straight  pipe 

35.09  diameters. 
Radius  of  elbow     1/2  diameter.     Equivalent  length  of  straight  pipe 

121.20  diameters. 

100.  Velocity  of  Compressed  Air  Flowing  Through  a  Pipe 
Line. — 

Let  Vc  =  volume  of  compressed  air  in  cubic  feet  per 

minute. 

v  =  velocity  in  feet  per  minute. 
A  =  area  of  pipe  section  in  square  feet. 

then  v  =  ~  ft.  per  minute.  (1) 


PIPE-LINE  EFFICIENCY  93 

If  in  Example  (2),  Art.  96,  the  average  pressure  of  the  air  is 

taken  as  ?? 

™        Fc     12.02     ___,  T7      2300X12.02 

Then  T  =  89J32     WhenCG  Fc=       89.52        =31°  CU'  ft' 

The  sectional  area  of  an  8-in.  pipe  is  0.35  sq.  ft. 

310 
Hence  y  =  ^-r^  =  885  ft.  per  min.  or  14.8  ft.  per  second. 

(J»oO 

Although  pressure  losses  in  a  pipe  line  are  obviously  a  function 
of  the  volume  of  air  transmitted  per  minute  and  therefore  of 
velocity,  as  well  as  of  the  length,  the  diameter  and  roughness 
of  the  pipe  line,  the  individual  effect  of  these  factors  has  not  as 
yet  been  definitely  determined.  It  is  generally  conceded, 
however,  that  for  economical  transmission  the  actual  velocity  of 
the  air  in  a  line  constructed  for  long  continuous  operation  should 
not  materially  exceed  30  ft.  per  second.  If  either  the  diameter 
of  the  pipe  or  the  volume  of  the  air  to  be  transmitted  are  fixed, 
the  velocity  is  decreased  in  the  first  case  by  limiting  the  volume 
of  air,  and  in  the  second  case  by  increasing  the  diameter  of 
the  pipe. 

100 A.  The  Planning  of  a  Transmission  Line. — It  has  been 
shown  that  the  transmission  of  compressed  air  involves  numerous 
losses  depending  on  the  size,  length  and  roughness  of  the  pipe, 
on  the  number  of  bends  and  elbows,  on  the  volume  of  air  to  be 
transmitted  and  the  initial  pressure  with  which  it  enters  the  pipe 
line. 

The  intelligent  planning  of  the  pipe  line  should  therefore 
aim  to  minimize  these  losses  as  much  as  practicable  by  trans- 
mitting the  air  to  the  points  of  use  over  the  shortest  possible 
route,  requiring  the  least  number  of  elbows,  joints  and  other 
obstructions,  and  by  selecting  this  route  so  that  the  pipe  is  access- 
ible at  all  points.  This  is  desirable  to  permit  frequent  inspection 
and  stoppage  of  leaks  which,  as  a  rule,  are  the  chief  cause  of 
extreme  pressure  losses. 

It  usually  pays  to  do  a  certain  amount  of  grading  and  excavat- 
ing in  order  to  eliminate  sudden  changes  in  both  the  horizontal 
and  vertical  alignments  of  the  pipe  line. 

If  air  is  to  be  transmitted  through  a  network  of  pipes,  not 


94  COMPRESSED  AIR 

only  the  diameter  of  the  air-main  but  the  diameters  of  all  the 
branch  pipes  should  be  calculated  with  the  highest  degree  of 
accuracy. 

This  is  accomplished  by  applying  the  formulas  in  Art.  96  to 
both  types  of  pipes. 

Example. — A  compressor  furnishes  to  a  mine  air  that  has  a  pressure 
of  100  Ib.  absolute  at  the  intake  terminal  of  a  6-in.  air  main.  The  free- 
air  equivalent  is  3000  cu.  ft.  per  min.  At  a  point,  26CO  ft.  from  the 
compressor  (measured  along  the  pipe  line)  a  1200-ft.  branch  line  is 
to  be  taken  off  to  supply  air  at  87  Ib.  absolute  to  six  stojing  drills, 
whose  combined  free-air  consumption  is  300  cu.  ft.  per  min.  What 
should  be  the  diameter  of  the  branch  pipe? 

For  the  solution  of  this  problem  it  is  necessary  to  know  the  normal 
air  pressure  at  the  point  of  take-off.  In  an  existing  pipe  line  the  pressure 
may  be  obtained  by  attaching  a  pressure  gage  to  the  air  main  at  that 
point.  But  if  the  branch  pipes  are  to  be  planned  simultaneously  with 
the  main  pipe,  the  expected  pressure  at  the  point  of  take-off  must  be 
calculated  by  equation  (6)  Art.  96. 


P. 

The  minimum  diameter  of  the  branch  pipe  will  be  from  equation  (2), 
Art.  96 

n    ' 


-  - 

^2000(922-872)     ' 

A  pipe  smaller  than  that  would  supply  neither  the  required  quantity 
of  air  nor  the  required  pressure. 

PIPE-LINE  EFFICIENCY 

101.  The  efficiency  of  a  pipe  line  is  the  ratio  between  the 
available  energy  for  doing  useful  work  residing  in  the  air  at  the 
discharge  end,  and  that  which  is  available  at  the  in- take  end  of  the 
line. l  In  computing  this  ratio  the  temperature  of  the  compressed 
air  must  be  assumed  to  be  the  same  at  both  terminals  of  the  pipe 
line.  For,  whatever  the  dimensions  of  the  pipe,  the  compressed 

1  See  also  Article  102. 


PIPE-LINE  EFFICIENCY  95 

air  at  the  discharge  end  will  be  practically  at  outside  temperature, 
that  is,  at  the  temperature  of  the  free  air  taken  into  the  com- 
pressor cylinder.  Any  extra  heat  left  in  the  compressed  air 
when  it  enters  the  pipe  line  should  be  charged  to  the  efficiency 
or  rather  the  inefficiency  of  the  cooling  devices  of  the  compressor 
and  the  receiver,  and  not  to  the  efficiency  of  the  pipe  line. 

The  maximum  energy  for  doing  useful  work  in  expanding 
isothermally  down  to  atmospheric  pressure,  which  resides  in  a 
given  weight  of  compressed  air  occupying  a  volume  ¥2,  is  the 
same  as  the  energy  expended  in  compressing  isothermally  that 
same  weight  of  free  air  to  a  given  pressure  and  delivering  it  under 
that  pressure  via  the  receiver  into  the  pipe  line. 

Let  Fi  =  volume  in  cubic  feet  of  a  given  weight  of  free  air  to  be 
compressed,  being  at  outside  temperature. 

PI  =  initial  absolute  pressure  in  pounds  per  square  inch. 

P2  =  final  absolute  pressure  in  pounds  per  square  inch. 

F2  =  volume  in  cubic  feet  of  the  same  weight  of  air  after 
being  compressed  isothermally  to  a  pressure  P2. 

Then  the  energy  residing  in  this  volume  F2  of  compressed  air 
after  leaving  the  compressor  and  at  the  entrance  of  the  pipe 
line  is: 

Energy  at  entrance  of  pipe  line  =  144  P\V\  loge  YT 

•p 
=  144  PiFi  loge  p~  foot-pounds. 

At  the  end  of  the  pipe  line  this  volume  F2  owing  to  the  loss 
of  pressure  due  to  friction  and  other  causes,  has  expanded  into  a 
volume  Vs,  whereas  the  pressure  has  decreased  to  a  pressure  P3. 

The  energy  residing  in  this  volume  F3  at  a  pressure  P3  for  doing 
useful  work  is  the  same  as  the  energy  that  would  have  been 
expended  in  compressing  isothermally  a  volume  Fi  of  free  air 
from  a  pressure  PI  to  a  pressure  P3  and  delivering  the  compressed 
air  which  now  occupies  a  volume  F3  via  the  receiver  into  the  pipe 
line. 

That  is,  energy  residing  in  the  compressed  air  at  the  end  of  the 
pipe  line: 

Wn  =  144  PtVi  \oge  ~     =  144PxFi  loger  foot-pounds. 


96  COMPRESSED  AIR 

Hence  efficiency  of  pipe  line 


_  _ 

144PjTMog.pl 


and  since  the  modulus  cancels 


*-—    '  CD 

*>*% 

As  P3  is  always  smaller  than  P2  it  would  appear  from  formula 
(1)  that  the  efficiency  of  a  pipe  line  of  certain  dimensions  becomes 
smaller,  the  higher  the  pressure  P2  is  at  which  the  compressed  air 
enters  the  pipe  line.  This  would  be  true  if  P3  remained  the  same 
when  Pa  is  being  increased. 

According  to  equation  (6),  Art.  96,  however,  the  terminal 
pressure  and  therefore  the  potential  energy  of  the  air  at  the 
discharge  end  of  the  pipe  line  increases  with  the  increase  of 
the  initial  pressure,  and  so  does  the  pipe  line  efficiency. 

The  subsequent  loss  of  energy  due  to  the  fact  that  the  ex- 
pansion of  the  compressed  air  in  the  air  engine  will  be  adiabatic 
instead  of  isothermal,  must  be  charged  to  the  efficiency  of  the 
air  engine  or  to  the  whole  system,  but  not  to  the  pipe  line. 

Example.—  What  is  the  efficiency  of  a  6-in.  pipe  line,  1200  ft.  long, 
delivering  at  its  terminal  a  free-air  equivalent  of  4000  cu.  ft.  per  minute 
at  a  pressure  of  92  Ib.  gage?  Atmospheric  pressure  =  14.7  Ib. 

Introducing  in  equation  (5),  Art.  96,  the  proper  subscripts,  the  re- 
quired initial  pressure  will  be 


Then 

Whence  E  =  j°|  ^  =  0.975  or  98  per  cent. 

The  pressure  loss  in  this  case  is  112.34-106.70  =  5.64  Ib. 

If  the  same  quantity  of  air  were  transmitted  through  the  same  pipe 


PIPE-LINE  EFFICIENCY  97 

line  with  an  initial  pressure  of  130  Ib.  abs.  the  end  pressure  according  to 
equation  (6),  Art.  96,  would  be: 


showing  a  pressure  loss  of  only  130.0  —  125.5  =  4.50  Ib. 

This  indicates  that,  other  things  remaining  the  same,  higher  initial 
pressures  result  in  higher  pipe  line  efficiency. 

101A.  Resume  of  Pipe  Line  Computations. — As  has  been  pointed  out,  one 
of  the  chief  difficulties  of  accurate  pipe  calculation  lies  in  the  fact  that  com- 
pressed air,  while  flowing  through  a  pipe,  creates  friction  which  gradually 
but  persistently  decreases  the  pressure  of  the  air.  This  loss  of  pressure  is 
accompanied  by  a  corresponding  expansion  of  the  air,  that  is,  by  an  increase 
in  volume.  To  transmit  this  increased  volume  through  the  pipe,  requires 
increased  velocity  of  flow  resulting  in  a  further  increase  of  friction  loss 
and  so  on. 

Mathematical  formulas  for  general  use  must  of  necessity  assume  more  or 
less  uniform  conditions.  In  the  pipe  line  formulas  it  is  assumed  that  fric- 
tion losses  are  directly  proportional  to  the  length  of  the  pipe.  That  is,  if  a 
loss  of  8  Ib.  occurs,  for  instance,  in  a  pipe  5.85  in.  in  diameter  and  1200  ft. 
long,  transmitting  a  free-air  equivalent  of  4000  cu.  ft.  per  min.  (Example  1, 
Art.  96),  then  a  loss  of  16  Ib.  would  be  found  from  the  formulas  for  a  2400 
ft.  pipe  line  of  the  same  diameter  and  transmitting  the  same  amount  of  air 
at  the  same  initial  pressure. 

The  assumption  implies  that  the  velocity  of  flow  is  the  same  at  all  points 
in  the  line,  which  would  only  be  the  case  if  the  pipe  line  were  constructed 
with  a  gradually  increasing  cross-sectional  area,  corresponding  to  the  in- 
crease in  volume  mentioned  above.  This  is,  of  course,  impracticable  in 
commercial  operations. 

Although  the  pressure  loss  due  to  friction  increases  with  the  length  of  the 
pipe,  the  number  of  elbows  and  other  obstructions,  the  actual  loss  in  any 
particular  section  of  the  pipe  line  is  greater  than  that  in  the  preceding  one, 
.not  in  direct  proportion  to  the  length  of  the  pipe  but  in  a  proportion  that 
eludes  statement  by  simple  mathematical  formulas.  The  shorter  the  pipe 
line,  the  more  nearly  correct  will  be  the  results  obtained  from  the  formulas, 
because  the  more  nearly  uniform  will  be  the  conditions  between  the  intake 
and  the  discharge  terminal  of  the  pipe  line.  The  longer  the  pipe  line,  the 
greater  will  be  the  discrepancies  between  the  results  obtained  by  the  form- 
ulas and  those  obtained  in  practice.  Hence  the  necessity  of  making  suffi- 
cient allowance  for  the  many  incalculable  factors  such  as,  for  instance,  the 
roughness  of  the  pipe  and  the  obstructions  the  air  meets  at  each  joint  of  the 
pipe  line.  Unsatisfactory  results  in  long  transmission  lines  are  frequently 
due  to  failure  to  realize  the  magnitude  of  the  pressure  losses  caused  by  these 
factors. 

No  general  rule  can  be  laid  down  as  to  the  proper  allowances  to  be  made 
in  each  individual  case.  All  that  may  be  said  is,  that  it  usually  pays  to  in- 
crease the  diameter  of  the  pipe  beyond  that  obtained  by  calculation  up  to  a 
point  at  which  the  economic  advantages  gained  no  longer  balance  the  extra 
cost  of  installation. 


98  COMPRESSED  AIR 

102.  Effect  of  Altitude  on  Pipe-line  Efficiency.— In  making 
estimates  of  pipe-line  efficiency  it  must  be  borne  in  mind  that  so- 
called  losses,  due  to  difference  of  elevation,  as  explained  under 
Article  97  cannot  be  charged  to  the  efficiency  of  the  pipe  line. 
For  the  pressure  loss,  due  to  the  difference  of  elevation  is  a  con- 
stant quantity,  no  matter  what  the  dimensions  of  the  pipe  line 
may  be.     This  loss  must  be  charged  to  the  compressed-air  instal- 
lation as  a  whole  as  pointed  out  in  Article  121. 

103.  Final  Dimensions  of  Pipe  Line. — In  any  individual  instal- 
lation, the  length  of  the  pipe  line  is  generally  a  given  quantity 
as  well  as  the  amount  of  air  that  must  be  delivered  at  a  certain 
pressure  at  the  end  of  it.     We  have  seen  that  high  initial  pressures 
give  high  pipe-line  efficiency,  but  require  more  powerful  and 
more  expensive  compressors.     On  the  other  hand,  with  low  initial 
pressure,  a  more  expensive  pipe  line  of  larger  diameter  is  required 
in  order  that  the  pressure  at  the  discharge  end  may  be  a  definite 
quantity. 

Since  the  power  residing  in  compressed  air  depends  on  the  pres- 
sure as  well  as  on  the  volume,  and  since  in  a  pipe  line  the  decrease 
in  pressure  is,  up  to  a  certain  point,  greater  than  the  loss  of  power, 
it  is  a  question  whether  it  is  more  economical  to  have  a  high  initial 
pressure  and  a  smaller  pipe  line  or  a  lower  initial  pressure  and  a 
larger  pipe  line. 

In  general,  the  decision  in  favor  of  the  one  or  the  other  must  be 
made  by  taking  into  consideration  a  number  of  factors  and  by 
comparing  the  costs  for  each  individual  case. 

In  making  these  computations  it  must  also  be  borne  in  mind 
that  the  power  required  to  compress  air  to  a  certain  pressure  is 
not  in  direct  proportions  to  these  pressures  themselves  as  pointed 
out  under  Article  49. 

Under  certain  conditions  it  may  be  more  economical  in  the  end 
to  have  high  initial  pressures  with  a  smaller  size  pipe  line.  Under 
other  conditions  the  reverse  may  be  the  case.  This  is  a  problem 
which  can  be  only  solved  after  due  consideration  of  all  the  condi- 
tions which  affect  the  plant  to  be  installed,  such  as  cost  of  pipes, 
cost  of  fuel,  transportation,  labor,  etc.,  and  the  probable  life  of 
the  plant. 

104.  Pipe -line  Construction. — From  what  has   been   said  re- 
garding losses  in  the  transmission  of   compressed   air   through 
pipes,  it  is  evident  that  not  only  the  design  of  a  pipe  line  should 


PIPE-LINE  CONSTRUCTION  99 

be  given  due  attention,  but  that  the  laying  of  the  line  should 
also  receive  considerable  care. 

Friction  being  the  chief  cause  of  loss  in  an  otherwise  well- 
proportioned  and  constructed  pipe  line,  it  is  desirable  that  the  in- 
terior of  the  pipe  should  be  as  smooth  as  possible.  In  ordering 
pipes,  particular  mention  should  be  made  that  the  interior  of  the 
pipes  should  be  free  from  all  roughness  such  as  scale,  blisters, 
lumps,  etc.,  and  when  the  piping  is  put  up,  great  care  should  be 
taken  to  clean  the  lengths  thoroughly  of  dirt  which  may  have 
gotten  into  them. 

Where  the  line  is  exposed  to  severe  cold,  the  moisture  in  the 
air  will  condense  and  the  water  so  formed  will  freeze  in  the  pipes 
until  it  throttles  or  chokes  the  pipe  altogether.  Since  this  takes 
place  particularly  in  low  points  of  the  pipe  line  which  form  pockets 
for  the  accumulation  of  the  entrained  water,  such  pockets  should 
be  avoided  as  much  as  possible. 

Valves  and  bends  will  increase  the  friction  to  a  great  extent. 
A  globe  valve  causes  the  greatest  loss  and  an  ell  or  tee  causes  a 
loss  of  one-half  to  two-thirds  that  of  a  globe  valve.  Consequently 
care  should  be  taken  that  gate  valves  be  used  instead  of  globe 
valves,  and  as  few  bends  put  in  as  possible.  Where  turns  are 
absolutely  necessary  they  should  be  made  with  as  long  a  sweep  as 
possible,  either  by  bending  the  pipe  without  kinking  it  or  by 
using  long-sweep  ells  or  tees. 

Long  pipe  lines  which  are  exposed  to  high  temperatures  should 
be  provided  with  expansion  joints  to  avoid  springing  leaks. 
Leaks  should  be  attended  to  as  soon  as  discovered.  They  cause 
the  air  in  the  pipes  to  expand  and  to  lose  pressure  rapidly. 

The  heavy  losses,  caused  by  leaks  in  a  pipe  line  will  become 
clear  by  a  study  of  Article  105  and  the  numerical  example  con- 
tained therein. 

FLOW  OF  COMPRESSED  AIR  FROM  AN  ORIFICE  INTO  THE 
ATMOSPHERE 

105.  Let  the  confined  air  be  under  a  pressure  of  "p"  pounds 
gage.  The  theoretical  velocity  with  which  it  flows  from  an 
orifice  into  the  atmosphere  is: 

v  =  yl2gh  feet  per  second.  (1) 

in  which  v     =  velocity  in  feet  per  second. 

g    =  acceleration  due  to  gravity  =  32.2  ft.  per  second. 


100  COMPRESSED  AIR 

h    =  height  in  feet  of  a  column  of  air  of  uniform  density, 
corresponding  to  a  gage  pressure  p  and  exerting 
a  pressure  of  p  pounds,  on  its  base  which  is  assumed 
to  be  1  sq.  in.  in  area. 
The  volume  V  of  this  column  is : 

V  =  ^h  cubic  feet.  (2) 

It  is  evident  that  the  mass  of  air  forming  this  column  must 
weigh  p  pounds  in  order  to  exert  a  pressure  of  p  pounds  per  square 
inch  which  is  the  area  of  its  base. 

According  to  Article  2  the  weight  W  of  1  cu.  ft.  of  atmospheric 
air  at  60°  Fahr.  is  0.0764  Ib.  The  weight  Wi  of  1  cu.  ft.  of  air 
having  a  density  corresponding  to  a  gage  pressure  p,  we  find  from 
Article  22: 

Wi=  p+14.7 
W  ~      14.7 
whence 


Wi  =  0.0761      147     Ib.  per  cubic  foot, 

Since  the  total  weight  of  the  air  column  must  be  p  pounds,  its 
volume  must  be: 

V  =  —  J-T-  =•  cubic  feet. 

0.0764^y4-l 

Combining  equations  (2)  and  (3),  we  have: 

JL=      _p_ 

144  ~  0.0764^7- 
14.7 


whence  A  = 

'    0.0764(p+14.7) 


Introducing  this  value  in  equation  (1)  we  get: 
v  =  ^2X32.2X27,707 


p+14.' 


FLOW  OF  COMPRESSED  AIR  THROUGH  AN  ORIFICE    101 


or,  theoretical  velocity  v  =  1336^1 £-—  feet  per  second         (5) 

The  actual  velocity  is,  of  course,  less  owing  to  friction  and  other 
causes.  It  is  obtained  by  multiplying  the  theoretical  velocity 
by  an  orifice  coefficient  "  c."  For  ordinary  compressed  air 
problems  such  as  leaks  in  receivers  and  pipe  lines,  where  the 
pressures  range  from  five  to  ten  atmospheres,  this  coefficient 
may  be  taken  as 

c  =  0.50 

This  gives  for  actual  velocity: 

v  =  1336X0.50A/— 


or  =  668    —~  feet  per  second.  (6) 


The  volume  V\  of  compressed  air  in  cubic  feet  per  minute, 
that  flows  from  an  orifice  of  the  area  "a"  square  feet  is: 


or  FI  =  40,080  X  cu  /  -  —  -  cu.  ft.  of  compressed  air  per  min.  (7) 

After  expansion  to  atmospheric  or  free  air,  and  after  having 
assumed  outside  temperature,  the  volume  Fi  of  compressed  air 
will  occupy  a  volume  Va  which  we  find  from  Article  15  as  follows: 

Z?-^ 
F!     Pa 

whence  Fa=F^  (8) 

Jt  a 

in  which  Pa   =  atmospheric  pressure  in  pounds  per  square  inch 

=  14.7. 
PI   =  absolute  pressure  of  compressed  air  in  pounds 

per  square  inch  =  p  +  14.7. 
Introducing  values  in  equation  (8)  we  get  : 

40,080(p+14.7) 
Va~'          14.7 


or  Va  =  2727  a  Vp(p+ 14.7)   cubic  feet  (9) 

of  free  air  per  minute  at  outside  temperature. 


102  COMPRESSED  AIR 

in  which     a  =  area  of  orifice  in  square  feet. 

p  =  gage  pressure  of  compressed  air  in  pounds  per 
square  inch. 

Example.  —  Air  under  pressure  of  80  Ib.  gage  escapes  from  various 
leaks  in  a  pipe  line.    What  is  the  quantity  of  escaping  air,  expressed 
in  cubic  feet  of  free  air  per  minute,  when  the  combined  area  of  the 
leaks  is  1/2  sq.  in.? 
In  this  case 

0.50 
a  -  sq.ft. 


Therefore  Va=  V80(8Q+1AJ)  =  824  cu.  ft. 

of  free  air  per  minute,  having  outside  or  in-take  temperature. 

If  the  compressor  is  built  to  furnish  1500  cu.  ft.  of  free  air  per 
minute,  the  leaks  in  the  pipe  line  will  cut  down  its  useful  capacity  to 
less  than  one-half,  without,  however,  cutting  down  the  power  required 
to  run  it. 

The  theoretical  horse-power  required  to  compress  in  two  stages  824 
cu.  ft.  of  free  air  per  minute  to  80  Ib.  gage  and  deliver  it  into  the 
receiver,  is  (from  column  7,  Table  V) 

824X0.141  =  116  h.p. 

which  represents  the  theoretical  power  loss,  due  to  the  leaks,  which  at 
first  sight  seem  rather  insignificant.  This  points  to  the  importance  of 
stopping  them  as  soon  as  discovered. 


PART  III 

THE  USE  OF  COMPRESSED  AIR 


CHAPTER  XII 
THEORY  OF  AIR  ENGINES 

106.  Compressed  air  can  be  used  to  operate  an  engine  in  a 
manner  similar  to  steam,  either  at  full  pressure  or  expansively. 
In  the  first  case  air  at  full  pressure  is  admitted  into  the  cylinder  of 
the  engine  during  the  entire  stroke  and  is  exhausted  practically 
at  full  pressure.     In  the  second  case  air  is  admitted  into  the 
cylinder  during  part  of  the  stroke,  is  then  cut  off  and  used  ex- 
pansively for  the  remainder  of  the  stroke.     In  practice  it  is 
always  exhausted  at  a  pressure  slightly  above  atmospheric  pres- 
sure for  reasons  stated  in  Article  112. 

107.  Compressed  Air  Used  at  Full  Pressure  During  the  Entire 
Stroke. — Although  the  efficiency  of  an  engine  using  air  in  this 
fashion  is,  of  necessity,  small,  the  waste  of  energy  in  such  engines 
is  usually  compensated  in  part  by  the  saving  in  first  cost  and 
labor,  due  to  the  simplicity  of  construction  of  such  machines  and 
the  ease  of  handling  them. 

108.  The  theoretical  net  work  in  foot-pounds  performed  per 
stroke  by  engines  using  air  at  full  pressure  during  the  entire 
stroke  is  equal  to  the  total  force  multiplied  by  the  distance 
through  which  it  acts. 

The  total  force  is :  (absolute  pressure  of  compressed  air  on  the 
in -take  side  minus  atmospheric  pressure  on  the  exhaust  side) 
multiplied  by  (area  of  piston).  The  distance  through  which  the 
force  acts  is  the  length  of  the  stroke. 

Let  Wn  =  net  work  in  foot-pounds. 

PI    =  absolute  pressure  of  air  in  pounds  per  square  inch  on 

in-take  side. 
Pa    =  atmospheric  pressure  in  pounds  per  square  inch  on 

exhaust  side. 

A     =  area-  of  piston  in  square  feet. 
L     =  length  of  stroke  in  feet. 
Vi    =  volume  of  compressed  air  in  cubic  feet  taken  into  the 

cylinder  per  stroke. 

105 


IQQ  COMPRESSED  AIR 

Then  Wn  =  144(P!-Pa)XAL 

And  since  AL  =  V\ 

Wn  =  144  (Pi  -Pa)  Fi  foot-pounds. 

Assume  that  the  volume  Fi  of  air  required  to  do  this  work  is 
obtained  by  isothermal  compression,  then  the  work  of  supplying 
this  volume  would  be  a  minimum,  viz: 

r> 

144  Pa  Fa  loge  p-1  foot-pounds 

LO. 

in  which  Fa  =  volume  of  free  air  which,  after  being  compressed 
isothermally  to  an  absolute  pressure  Pi  would  occupy  a  volume  Fi 

Therefore 

109.  Maximum  efficiency  of  air  engine  using  air  at  full  pressure 
during  the  entire  stroke  is: 

144  (Pi  -P0)  Fi       ^i^Pa 


Dividing  dividend  and  divisor  by  P0 


This  shows  that  the  higher  the  initial  pressure  Pi  at  which  the 
air  enters  the  air  engine,  the  smaller  becomes  the  efficiency. 

Example.  —  A  striking  example  of  an  apparatus  using  air  at  full  pres- 
sure during  the  entire  stroke  is  the  well-known  rock  drill.  In  consump- 
tion of  power  it  is  one  of  the  most  wasteful  machines,  but  from  a  prac- 
tical point  of  view  its  efficiency  stands  at  present  unquestioned. 

The  theoretical  efficiency  of  a  rock  drill  with  a  cylinder  of  3  1/4  in.  in 
diameter,  6  3/4-in.  stroke,  400  strokes  per  minute,  using  air  at  60  Ib. 
gage  is  as  follows: 
Area  of  piston  ..............................     8.29  sq.  in. 

Piston  displacement  8.29X6  3/4=  ...........   55.96  cu.  in. 

Volume  of  air  taken  into  cylinder  per  minute 

^y|g  X400=  ..............................   12.95  cu.  ft.  at  60  Ib. 

Volume  of  free  air,  equivalent  to  12.95  cu  ft.  at  60  Ib. 


Fa  =  12.95  =  ...............  65.8  cu.  ft.  per  min. 


THEORY  OF  AIR  ENGINES 

Theoretical  horse-power  required  to  compress 
and  deliver  65.8  cu.  ft.  per  min.  at  60  Ib.  gage 

(from  column  4,  Table  V)  65.8X0.134= 8.8  h.p. 

Power  utilized  in  striking  rock  (forward  stroke 


107 


only),  8.29X60X 


63/4X200 
12 


....  56,200  ft.-lb. 


=      1.70  h.p. 

In  this  case  the  theoretical  efficiency  of  the  drill  is  only  19  per  cent. 
The  practical  efficiency  will  be  much  less,  due  to  friction  leakage,  etc., 
in  the  drill  itself  and  to  power  losses  in  bringing  the  air  to  the  drill. 

COMPRESSED  AIR  USED  WITH  COMPLETE  ADIABATIC 
EXPANSION 

110.  The  theoretical  net  work  performed  per  stroke  by  engines 
using  air  with  complete  adiabatic  expansion  down  to  atmospheric 
pressure,  is  deduced  in  the  same  manner  as  that  for  compression. 


FIG.  15. 


Referring  to  Fig.  15: 

Wn  =  144  X  (shaded  area  A  BCD)  foot-pounds 
But  area  ABCD  =  area  ABFE 
plus  area  FBCG 
minus  area  EDCG 
Area  ABFE  =  P2VZ 


r 
PdV 


r° 

=    \Pc 

JV* 


108  COMPRESSED  AIR 

But  PVn  =  P, 


hence  area  FBCG  = 


fk 

Jv,  y" 


v, 


=  P2  J  Y  I  V 

Jvt 


va 
V~"dV 


1-n 

and  since     P2F2n  =  PaVan 
we  can  write: 


l-n 


n-1 
area  EDCG  =  PaVa 

therefore          Wn  =  144  (P2F2+P2^^p~-P07a) 
144  n 


and  since  ~  =  ( -=?  ]  " 


n-l-. 

~  IP")  "      foot-pounds.    (1) 


THEORY  OF  AIR  ENGINES  109 

in  which  W „  =  net  work  in  foot  pounds  per  stroke. 

P2  =  absolute   pressure    in   pounds    per    square 

inch  of  compressed  air  entering  cylinder. 
Vt  =  volume   of    compressed    air   in   cubic  feet 

taken  into  the  cylinder  per  stroke. 
Pa  =  atmospheric  pressure  in  pounds  per  square 

inch. 
n=  1.406. 

111.  The  theoretical  horse-power  which  a  volume  Vz  of  air 
in  cubic  feet  per  minute,  compressed  to  an  absolute  pressure  P2 
is  capable  of  developing  during  admission  and  adiabatic  ex- 
pansion to  atmospheric  pressure,  is  obtained  by  letting  F2  in 
the  formula  for  Wn  represent  the  number  of  cubic  feet  per  minute 
admitted  into  the  cylinder  and  by  dividing  the  whole  by  33,000. 


(1) 


Theoretical  horse-power  -  33^%  [l-  (g)  "  ] 

in  which  P2  =  absolute  pressure  in  pounds  per  square  inch  of  air 

entering  cylinder. 
F2  =  volume  of  compressed  air  taken  into  the  cylinder 

in  cubic  feet  per  minute. 

Pa  =  atmospheric  pressure  in  pounds  per  square  inch. 
n  =  1.406. 

112.  In  practice  complete  expansion  to  atmospheric  pressure 
is  not  feasible  for  the  following  reasons: 

1.  The  resulting  increase  in  volume  of  the  expanded  air  would 
require  a  more  expensive  engine  with  larger  cylinders  than  is 
warranted  by  the  small  gain  in  power. 

2.  To  overcome  the  friction  of  the  engine  near  the  end  of  the 
stroke  and  to  cause  the  air  to  properly  exhaust  against  the  back 
pressure  of  the  atmosphere,  the  pressure  of  the  exhaust  air  must 
be  somewhat  greater  than  the  atmospheric  pressure. 

3.  Unless  the  compressed  air  is  reheated  before  being  used,  its 
temperature  when  entering  the  air  cylinder  of  the  engine  is  that 
of  the  surrounding  atmosphere.     A  high  ratio  of  expansion  will 
result  in  very  low  final  temperature  and  quite  often  in  freezing 
of  the  moisture  in  the  air  around  the  exhaust  ports. 

Example. — Assuming  that  air  at  80  Ib.  gage  and  60°  Fahr.  enters  the 
cylinder  of  an  air  engine  and  that  it  is  allowed  to  expand  adiabatically 


110 


COMPRESSED  AIR 


to  atmospheric  pressure  at  sea  level,  then  the  theoretical  final  absolute 
temperature  of  the  exhaust  air  would  be: 


(60+461) 


=305°  absolute. 
=  -156°  Fahr. 


COMPRESSED  AIR  USED  WITH  PARTIAL  ADIABATIC  EXPANSION 

113.  For  reasons  stated  in  Article  112,  air  engines  usually 
work  with  partial  expansion,  that  is,  a  volume  of  compressed  air 
is  admitted  during  part  of  the  stroke,  is  then  cut  off  and  allowed 
to  expand  down  to  a  pressure  somewhat  above  atmospheric 
pressure. 


FIG.  16. 

Referring  to  Fig.  16  the  net  work  performed  during  one  stroke 
of  the  piston  is: 

Wn  =  144  X  (shaded  area  ABHKD^ 
But  area  ABHKD  =  area  EABF=P2V2 

plus  area  FBHM=^^^ 
n—  1 


minus  area  DEMK=PaVi 


whence    Wn  = 


foot.pounds> 


in  which  P2  =  initial  absolute  pressure  in  pounds  per  square 
inch  of  air  entering  engine. 


THEORY  OF  AIR  ENGINES  111 

F2  =  volume  of  compressed  air  in  cubic  feet  taken  into 

the  cylinder  per  stroke. 
PI  =  absolute  pressure  in  pounds  per  square  inch  of 

exhaust  air. 
Vi  =  volume  of  air  exhausted  per  stroke  at  a  pres- 

sure PI. 

Pa  =  atmospheric  pressure  in  pounds  per  square  inch. 
n  =  1.406. 

114.  Mean  gage  pressure  of  air  during  admission  and  partial 
adiabatic  expansion: 

W  V     P*~ 


Pa     P°unds  Per  S(}uare  inch- 


n-l 


115.  Theoretical  horse-power  which  a  volume  of  compressed 
air  per  minute  is  capable  of  developing  during  admission  and 
partial  adiabatic  expansion: 


in  which,  P2  =  absolute  pressure  in  pounds  per  square  inch  of 
in-take  air. 

F2  =  volume  of  compressed  air  in  cubic  feet  taken  into 
the  cylinder  per  minute. 

PI  =  absolute  pressure  in  pounds  per  square  inch  of  ex- 
haust air. 

Fi  =  volume  of  air  exhausted  at  a  pressure  P\  in  cubic 
feet  per  minute. 

Pa  =  atmospheric  pressure  in  pounds  per  square  inch. 
n  =  1.406. 

In  practical  problems  P2,  F2  and  Pa  are  always  known,  and 
either  Pi  or  V\  are  given. 

If  PI  is  given,  then  Fi  is  found  from  the  relation: 

Vi      /P,\S- 


whence 


112  COMPRESSED  AIR 

If  Fi  is  given,  as  in  engines  having  a  certain  cut-off,  then 
is  found  from  the  relation: 


whence  Pi  —  P*\ 

Example. — Find  theoretical  horse-power  developed  by  1  cu.  ft.  of 
air  per  minute,  having  a  pressure  of  100  Ib.  gage,  being  admitted  to 
and  expanded  adiabatically  in  an  air  engine  with  1/4  cut-off.  Atmos- 
pheric pressure  =  14.7  Ibs. 

For  1/4  cut-off  Fj  =  4F2  =  4  cu.  ft. 

and  P:  =  (100+ 14.7)  (1/4)  »•«•  =  16.3  Ib.  per  sq.  in. 

n,7+  i 

116.  Modified  Power  Values  for  Practical  Air-engine  Prob- 
lems.— In  practical  computations,  the  theoretical  formulas,  ex- 
pressing the  energy  residing  in  a  quantity  of  compressed  air 
for  doing  useful  work,  must  be  modified  for  the  same  reasons 
explained  in  Article  74. 

It  is  customary  to  subtract  15  per  cent,  from  the  theoretical 
values  in  order  to  obtain  the  actual  work  that  an  air  engine  may 
be  expected  to  perform  under  normal  conditions. 


CHAPTER  XIII 

EFFECT    OF   LOSS    OF    HEAT,    GENERATED    DURING    COM- 
PRESSION,   ON   THE    ULTIMATE   USEFUL  ENERGY    RE- 
SIDING IN  A  GIVEN  QUANTITY  OF  COMPRESSED  AIR 

117.  By  an  accepted  law  of  thermodynamics,  work  and  heat 
are  mutually  convertible  at  the  ratio  of  about  778  ft.-lb.  of  work 
for  every  B.T.U. 

In  Article  41  a  it  was  stated  that  the  work  expended  in  com- 
pressing air  is  all  converted  into  heat.  According  to  the  law 
quoted,  we  should  expect  the  compressed,  and  therefore  heated, 
air  to  be  capable  of  performing  useful  work,  equal  to  the  amount 
expended  in  compressing  it.  Neglecting  friction  in  the  air 
engine,  this  would  actually  be  the  case,  if  the  compressed  air  could 
be  used  immediately  after  compression  and  before  it  has  lost 
any  of  its  heat. 

If,  on  the  other  hand,  the  compressed  air  be  allowed  to  cool 
down  to  the  temperature  which  it  possessed  before  compression, 
as  happens  in  all  compressed  air  installations,  it  would  seem 
logical,  by  applying  the  same  law  quoted  above,  to  reason  as 
follows : 

Since  the  work  of  compression  is  all  converted  into  heat,  the 
ability  for  doing  useful  work  must  have  disappeared  after  all 
this  heat  has  been  abstracted. 

In  the  following  articles  it  will  be  shown: 

a.  That  the  work  of  compression  is  all  converted  into  heat. 

6.  That,  after  all  the  heat  of  compression  has  been  abstracted, 
there  still  remains  in  the  compressed  air  a  certain  amount  of 
energy  for  doing  useful  work. 

c.  That  this  is  due  to  the  energy  residing  in  the  air  before 
compression. 

a.  Referring  to  Fig.  17,  the  total  work  of  compressing  adia- 
batically  a  volume  V\  cubic  feet  of  free  air  from  an  absolute  pres- 
sure PI  to  an  absolute  pressure  P2  is  represented  by  the  area 
MABR.  Expressed  in  foot-pounds,  it  is  equal  to  144  times  the 
numerical  value  of  this  area. 

s  113 


114  COMPRESSED  AIR 

In  Article  44  we  found: 

Area  MA  BR  =  -*— ^ 

n —  l 

therefore,  total  work  of  compression 
V      p  V, 
— ~~i foot-pounds. 


(1) 


(2) 


Let   Pi  =  H.7  Ib.  absolute  pressure  per  square  inch. 
Pz  =  89.7  Ib.  absolute  pressure  per  square  inch. 

=  75  Ib.  gage. 
Vi  =  13.09  cu.  ft.  which  is  the  volume  of  1  Ib.  of  free  air  at 

sea  level  and  at  60°  Fahr. 
n  =  1.406. 


K-  V,—- 


FIG.  17. 
From  equation  (7),  Article  41,  deduce: 


whence      V*  =  Vi(jrJ     =13.09(^j       =3.62  cu.  ft.  (3) 

Substituting  values  in  equation  (2)  we  get: 

b.  (4) 


EFFECT  OF  LOSS  OF  HEAT  115 

After  the  air  has  been  compressed  adiabatically  to  an  absolute 
pressure  PZ  its  absolute  temperature  will  be  according  to  equation 
(11),  Article  41: 


0.29 


T2  =  T1   j          =  (60+461)   —  j       =  880°  absolute      (5) 

=  419°Fahr. 

After  compression,  the  original  pound  of  air  occupies  a  volume 
F2  =  3.62  cu.  ft.  and  has  a  temperature  of  419°  Fahr.  which  is 
(419  —  60)  =359  degrees  more  than  its  initial  temperature. 

Now,  we  can  imagine  a  volume  72  of  air  weighing  1  Ib.  to  have 
a  temperature  of  60°  Fahr.  If  we  raise  the  temperature  of  this 
air  by  (Tz-TJ  =  (880-561)  =359  degrees  without  changing  its 
volume,  we  heat  under  constant  volume.  The  specific  heat  Cv 
of  air  in  this  case  is  0.168  and  the  amount  of  heat  put  into  this 
pound  of  air,  expressed  in  B.T.U.'s.  is 

C^Tz-TJ  =0.168X359  =  60.3  B.T.U.'s. 
Expressed  in  foot-pounds  it  is: 

K^Tz-TJ  =  131.6X359  =  47,000  ft.-lb.  (6) 

A  comparison  of  equation  (6)  with  (4)  shows  that  the  mechan- 
ical equivalent  of  the  heat  required  to  raise  the  temperature  of 
1  Ib.  of  air  from  an  absolute  temperature  TI  to  an  absolute 
temperature  Tz  is  identical  with  the  mechanical  energy  expended 
in  compressing  adiabatically  1  Ib.  of  atmospheiic  air  having  an 
absolute  temperature  TI  to  a  pressure  which  raises  the  tempera- 
ture of  the  air  to  an  absolute  temperature  TV  In  other  words, 
the  mechanical  work  of  compressing  air  adiabatically  is  all  con- 
verted into  heat  energy. 

b.  If  we  now  allow  this  volume  Vz  =  3.62  cu.  ft.  of  compressed 
air,  having  a  temperature  of  419°  Fahr.,  to  cool  down  to  initial 
temperature  of  60°  Fahr.  under  constant  volume,  its  pressure 
will  decrease  to  a  pressure  P3,  which  we  find  from  the  formula: 

m  KO1 

P=P±*  =  89.7x—  =  53.2  Ib.  absolute. 


The  energy  residing  in  this  volume  F3=3.62  cu.  ft.  of  air  for 
doing  useful  work  in  expanding  adiabatically  down  from  an 
absolute  pressure  of  53.2  Ib.  to  atmospheric  pressure  is  represented 


116 


COMPRESSED  AIR 


by  the  area  BCGF  in  the  diagram,  Fig.  18,  and  expressed  in 
toot-pounds  it  is  144  times  the  numerical  value  of  this  area. 
From  article  110  we  deduce: 


Hence  energy 


Area  BCGF 


W  =144 


n-l 

P3Vt-PiVi 
n-l 


FIG.  18. 

Applying  it  to  the  case  in  hand: 

P3  =53.2  Ib.  absolute  per  sq.  in. 

F2  =3.62  cu.  ft. 

PI  =  14.7  Ib.  per  sq.  in. 


(i    \  n  /^  2\ 

p-J    =  3.62(~J       =9.02cu.ft.    (From  equa- 
tion 13,  Article  41.) 


1.406. 


Hence  TF-144X  53.2X3.62- 14.7x9.02   =21300ft.,b 
0.406 

Comparing  this  with  the  work  of  compression,  we  have: 

21,300 
47,000 : 


EFFECT  OF  LOSS  OF  HEAT  117 

That  is,  theoretically,  after  cooling  down  to  initial  temperature, 
there  still  remains  in  the  compressed  air  energy  for  doing  expan- 
sive work  to  the  amount  of  45  per  cent,  of  the  energy  expended 
in  compressing  it. 

Referring  to  the  diagram  in  Fig.  17,  it  will  be  noted  that  part 
of  the  total  work  of  compression  represented  by  the  area  MABR 
is  performed  by  the  atmospheric  air  rushing  into  the  cylinder 
behind  the  piston  during  the  compression  stroke  and  not  by 
energy  furnished  by  the  compressor.  This  work  is  represented 
by  the  area  MAFR. 

In  practice,  the  air,  after  being  compressed,  is  delivered  into 
the  receiver.  The  work  of  delivery  is  jointly  performed  by  the 
compressor  and  by  the  atmospheric  air.  The  compressor's 
work  is  represented  by  the  area  FBCD  and  the  work  of  the  atmos- 
phere by  the  area  RFDO.  The  net  work  of  compression  and 
delivery  done  by  the  air  compressor  alone  is  represented  by  the 
area  A  BCD.  The  compressor's  share  of  delivery  work  is  always 
available  for  doing  useful  work  in  the  air  engine  because  in  forcing 
a  volume  of  compressed  air  from  the  air-cylinder  into  the  receiver, 
an  equal  volume  of  air  is  displaced  therein,  and  this  displacement 
process  is  extended  into  the  pipe  line  and  finally  into  the  air 
engine,  where,  in  making  room  for  itself,  this  volume  of  compressed 
air  drives  the  piston  forward,  and  thus  does  useful  work. 

It  may  be  asked:  What  becomes  of  the  energy  contributed 
by  the  atmospheric  air  toward  compression  and  delivery  which  is 
represented  by  the  area  MADO  in  Fig.  17? 

This  energy  is  actually  stored  up  in  the  compressed  air  when 
the  latter  leaves  the  compressor.  It  could  do  useful  work  if  it 
were  practicable  to  exhaust  the  air  from  the  engines  into  a  vacuum. 
But  since  we  must  exhaust  against  atmospheric  pressure,  the 
energy  is  consumed  in  the  process  of  exhaustion  and  is  therefore 
not  available  for  useful  work.  It  is  not  included  in  the  formulas 
expressing  power  to  be  furnished  by  the  compressor  because  it  is 
furnished  gratis  by  the  atmosphere;  and  it  is  not  included  in  the 
formulas  expressing  the  useful  work  which  a  volume  of  compressed 
air  can  perform,  because  it  is  not  available  for  such  work. 

The  following  example  shows  the  effect  of  heat  loss  upon  the 
total  power  stored  up  in  a  mass  of  air  by  the  compressor. 

Example. — To  compress  adiabatically  in  one  stage  100  cu.  ft.  of  free 
air  per  minute  at  sea  level  to  60  Ib.  gage  and  deliver  it  into  the 
receiver,  requires  (theoretically)  13.40  h.p.  (from  column  4  Table  V). 


118  COMPRESSED  AIR 

If  the  temperature  of  the  free  air  Was  60°  before  compression,  after 
compression  it  will  be  375°  Fahr.  (column  6  Table  V)  and  the  volume  of 
the  compressed  air  will  be  31.44  cu.  ft.  (column  5  Table  III) 

If  used  immediately  after  compression,  before  having  lost  any  heat, 
it  could  do  work  (theoretically)  to  the  amount  of  13.40  h.p.  by  expanding 
adiabatically  down  to  atmospheric  pressure. 

But  if  allowed  to  cool,  before  use,  to  initial  temperature  under  con- 
stant volume,  the  pressure  will  decrease  to  a  pressure  P3  which  we  find 
from  the  following  formula: 

P3=P2g=(60+14.7)^±^\  =  46.6  Ib.  absolute. 

A  volume  of  31.44  cu.  ft.  of  air  per  minute  at  46.6  Ib.  absolute,  if  allowed 
to  expand  adiabatically  down  to  atmospheric  pressure  could  perform 
(theoretically)  an  amount  of  work  found  from  equation  (1)  Article  111: 


144nP 


2V2     I  /^Wl 

*  -T)  [  1  '  \PJ       \ 


10.29T 
1_(14'7)         =6.30  h.p. 
V46.6/       J 


which  is  about  47  per  cent,  of  the  power  expended  in  compression  and 
delivery. 

When  friction  and  other  imperfections  are  taken  into  account,  this 
percentage  decreases  materially. 

Adding  15  per  cent,  to  the  power  of  production  we  get  15.43  h.p. 

Subtracting  15  per  cent,  from  the  available  theoretical  energy  we  get 
5.35  h.p.  and  the  comparative  value  shrinks  to  35  per  cent.  This  is 
further  diminished  by  losses  during  transmission  which  are  pointed  out 
under  Articles  93-94  and  97-105. 

c.  The  answer  to  the  question,  why  energy  still  remains  in  the 
compressed  air  after  all  the  heat  of  compression  has  been  dis- 
sipated, is  that  a  certain  capacity  for  work  resides  in  the  air 
which  is  due  to  the  latter's  ability  to  expand  when  the  proper 
conditions  prevail. 

Such  conditions  could  be  brought  about  by  confining  a  volume 
of  atmospheric  air  in  a  cylinder  under  a  piston  and  then  create  a 
partial  vacuum  on  the  other  side  of  the  piston;  the  atmospheric 
air  in  the  cylinder  would  expand  and  push  out  the  piston,  that  is, 
perform  work.  But  creating  a  vacuum  requires  extra  work,  and 
is  therefore  not  of  practical  application  in  air  engines. 

As  a  matter  of  fact,  after  all  the  heat  generated  during  compres- 
sion of  a  volume  of  air  has  been  dissipated,  the  compressed  air 
possesses  no  more  energy  than  it  did  before  compression,  but 


VALUE  OF  "n"  119 

part  of  the  energy  which  it  did   possess  has,   by  mechanical 
compression,  been  made  available  for  doing  useful  work. 

To  do  work,  however,  the  air  requires  energy  in  the  form  of 
heat  and  while  expanding,  it  consumes  heat  that  was  contained  in 
its  mass  before  compression.  As  a  consequence  the  temperature 
of  the  expanded  air  falls  below  that  of  the  surrounding  atmos- 
phere. The  amount  of  heat  consumed  is  equivalent  to  the 
amount  of  work  performed  and  equal  to  the  amount  of  heat  that 
would  be  generated  in  compressing  this  air  from  the  pressure  at 
which  it  exhausts  from  the  air  engine  to  the  pressure  at  which  it 
enters  the  same. 

The  consumption  of  heat  from  the  mass  of  the  expanding  air 
is  manifested  by  the  cold  created  in  and  around  the  cylinders  of 
an  engine  using  air  expansively.  Theoretically  this  is  exactly 
the  reverse  of  the  generation  of  heat  in  the  air  cylinders  of  a 
compressor. 

117a.  Determination  of  the  Value  of  "n,"  used  in  adiabatic 
compression  and  expansion  formulas: 

From  equation  (6),  Article  117,  we  have: 
Work  of  adiabatic  compression  of  1  Ib.  of  free  air: 

W  =  Kv(Tz-  Ti)  foot-pounds  (1) 

in  which  Kv  =  specific  heat  of  air  at  constant  volume,  expressed 

in  foot-pounds. 
T2  =  final   absolute  temperature  of  air   after  being 

compressed  to  an  absolute  pressure  P2. 
TI  =  initial  absolute  temperature  of  air  at  an  absolute 

pressure  Pi. 

In  the  diagram,  Fig.  17,  the  area  MABR  represents  the  mechan- 
ical work  of  compressing  a  volume  V\  of  air  from  an  absolute 
pressure  PI  to  an  absolute  pressure  P2,  the  volume  of  compressed 
air  being  Vz- 

From  equation  (1)  Article  117: 

Are*  MABR-^^^1-  (2) 

7  1  —  J. 

Let  PI  and  P2  be  the  absolute  pressures  in  pounds  per  square 
foot;  then  the  work  performed,  corresponding  to  area  MABR: 


*=}f  ot_pounds 
n—l 


120  COMPRESSED  AIR 

Let,  furthermore,  V\  and  Vz  represent  volumes  occupied  by  1  Ib. 
of  air  when  under  an  absolute  pressure  of  PI  or  P2  respectively; 
then  from  equation  (5)  Article  20: 

PiFi  =  RT, 
and  P272  =  RTZ 

Substituting  these  values  in  equation  (3)  we  have: 


_  R  [T2  -  RT\  _      _2-    i 
n-l  n-1 


From  equation  (7)  Article  20  we  have: 
R  =  KP-KV 
Substituting  in  equation  (4)  we  get: 


This  work  is  equal  to  the  work  expressed  by  equation  (1),  there- 
fore: 


whence  n=     -  (6) 

as  first  stated  under  Article  40. 


CHAPTER  XIV 
INTERNAL  OR  INTRINSIC  ENERGY  OF  AIR 

118.  A  capacity  for  doing  useful  work  by  expanding  against  an 
external  resistance,  resides  in  a  mass  of  air  as  long  as  its  tempera- 
ture is  above  the  absolute  zero.  A  pound  of  atmospheric  air 
at  60°  Fahr.  at  sea  level,  for  instance,  may  be  conceived  as  the 
outcome  of  a  pound  of  air  at  the  temperature  of  absolute  zero 
to  which  a  sufficient  amount  of  heat  has  been  supplied  to  raise 
its  temperature  by  (461+60)  =521°  Fahr.,  and  its  pressure  to 
14.7  Ib.  above  the  vacuum. 

According  to  a  law  of  thermodynamics,  quoted  in  previous 
articles,  the  heat  energy  in  this  pound  of  air,  corresponding  to  a 
temperature  of  521°  above  the  absolute  zero,  may  be  converted 
into  mechanical  energy  whenever  the  conditions  permit  it.  The 
capacity  of  air  of  performing  work,  due  to  its  temperature  above 
the  absolute  zero,  is  called  the  internal  or  intrinsic  energy  of  air. 
It  is  independent  of  pressure,  that  is,  a  pound  of  atmospheric 
air  at  a  temperature  of  60°  Fahr.,  has  the  same  intrinsic  energy 
as  a  pound  of  air  under  a  pressure  of  100  Ib.  having  the  same 
temperature  of  60°  Fahr.  (See  Articles  119  and  120.) 

When  applied  to  practice,  there  is  a  vast  difference,  however, 
between  the  pound  of  atmospheric  air  and  the  pound  of  air  at 
100  Ib.  pressure.  In  the  first  case  none  of  the  intrinsic  energy 
residing  in  the  air  is  available  for  useful  work  under  ordinary 
conditions,  whereas  in  the  second  case  a  portion  of  the  intrinsic 
energy  has  by  mechanical  compression  been  made  available  for 
such  work. 

This  may  be  better  understood  by  comparison  with  the  more 
familiar  generation  of  water-power.  Water  flowing  down  a 
river  possesses  intrinsic  energy,  that  is,  a  capacity  for  doing 
useful  work  when  the  proper  conditions  exist.  These  conditions 
are  brought  about  by  building  a  dam  across  the  river  which 
raises  the  water  level  and  thus  produces  a  head,  the  height  of 
which,  together  with  the  amount  of  water  delivered,  determines 
the  amount  of  useful  work  the  water  is  capable  of  performing. 
By  building  the  dam  we  have  added  nothing  to  the  intrinsic 

121 


122  COMPRESSED  AIR 

energy  of  the  water,  we  have  only  made  available  a  portion  of 
that  energy  for  performing  useful  work. 

In  an  analogous  manner,  by  compressing  air  isothermally, 
we  add  nothing  to  its  intrinsic  energy,  we  merely  make  a  portion 
of  that  energy  available  for  doing  useful  work.  In  actual  prac- 
tice, compression  is  more  or  less  adiabatic,  imparting  heat  energy 
to  the  air,  which,  however,  is  subsequently  lost  in  transmission. 
The  condition  of  the  air  before  use  is  therefore  the  same  as  after 
isothermal  compression. 

The  conception  of  internal  or  intrinsic  energy  indicates  that 
when  air  expands  without  doing  work,  it  loses  none  of  its  heat, 
because  the  intrinsic  energy  remains  unchanged.  The  truth 
of  this  fact  was  first  proved  experimentally  by  Joule  and  the  fact 
itself  is  known  as  Joule's  Law. 

119.  Intrinsic  Energy  of  a  Pound  of  Atmospheric  Air  at  a 
Temperature  of  60°  Fahr.  —  The  specific  heat  of  air  under  constant 
pressure  is  0.2375,  therefore  the  quantity  of  heat,  that  is,  the 
number  of  B.T.U.'s  required  to  raise  the  temperature  of  1  Ib.  of 
atmospheric  air  from  absolute  zero  to  60°  Fahr.  is: 

(461  +60)  X  0.2375  =  123.74  B.T.U.'s 

and  the  amount  of  work  corresponding  to  this  quantity  of  heat  is 
123.74X778  =  96,268  ft.-lb.  This  is  the  intrinsic  energy  of  1  Ib. 
of  atmospheric  air  at  60°  Fahr.,  none  of  which,  however,  is  avail- 
able for  useful  work  under  ordinary  circumstances. 

120.  Intrinsic  Energy  of  a  Pound  of  Air  at  100  Ib.  Gage  and 
at  60°  Fahr.  —  If  permitted  to  expand  adiabatically  down  to 
atmospheric  pressure  against  an  external  resistance,  this  pound 
of  air  would  perform  work  and  therefore  consume  an  amount  of 
heat  equal  to  the  amount  that  was  generated  during  adiabatic 
compression.     The  theoretical  temperature  of  the  air  after  expan- 
sion is  deduced  from  formula  (11)  Article  41: 


=  286.55  degrees  absolute. 
=  -174.45°  Fahr. 


The  drop  in  temperature  is  therefore  (60+174.45)  =234.45 
degrees  and  the  number  of  B.T.U.'s  consumed  during  expansion 
would  be  234.45X0.2375  =  55.68  B.T.U.'s. 


INTERNAL  OR  INTRINSIC  ENERGY  OF  AIR  123 

The  equivalent  of  55.68  B.T.U.'s  expressed  in  foot-pounds  is 
55.68X778  =  43,321  ft.-lb.  This  is  the  amount  of  intrinsic 
energy  residing  in  the  pound  of  compressed  air  which  is  available 
for  doing  useful  work. 

But  there  still  remains  energy  in  the  air  which  might  be  used 
if  it  were  possible  for  the  air  to  expand  down  to  the  absolute 
zero  of  pressure,  in  which  case  the  temperature  of  the  air  would 
drop  from  286.55  absolute  to  the  absolute  zero  of  temperature. 
This  represents  a  consumption  of  heat  units  equivalent  to 
(286.55X0.2375)  =68.065  B.T.U.'s  and  these  68.056  B.T.U.'s 
present  work  equivalent  to  (68.056X778)  =52,947  ft.-lb.  This 
latter  energy  is  not  available  for  useful  work  under  ordinary 
circumstances. 

The  total  intrinsic  energy  of  the  pound  of  air  at  100  Ib.  gage 
and  60°  Fahr.  is  (43,321  +  52,947)  =96,268  ft.-lb.  which  is  the 
same  as  the  total  intrinsic  energy  of  the  pound  of  atmospheric  air 
at  60°  Fahr. 


CHAPTER  XV 
THE  EFFICIENCY  OF  A  COMPRESSED-AIR  SYSTEM 

121.  This  is  evidently  the  ratio  between  the  ultimate  work 
performed  by  the  engine  using  compressed  air  and  the  power 
required  to  compress  that  air  in  the  compressor. 

In  computing  this  efficiency  all  the  possible  losses  must  be 
taken  into  consideration  which  may  occur  from  the  moment  a 
certain  quantity  of  air  enters  the  compressor  until  it  is  exhausted 
from  the  air  engine. 

These  losses  are  chargeable: 

1.  To  air  being  taken  into  the  compressor  from  the  engine 
room  rather  than  from  a  cooler  place.     This  results  in  a  lesser 
quantity  (weight)  of  air  being  taken  into  the  cylinder  per  stroke, 
thereby  increasing  the  power  required  to   compress   a   given 
quantity  of  air  per  unit  of  time.     This  loss  can  be  prevented  by 
making  adequate  provisions  for  the  air  in-take  from  the  coolest 
outside  place  around  the  compressor  building  (see  Article  87). 

2.  To  friction  in  the  compressor.     This  will  amount  ordinarily 
to  a  power  loss  of  from  15  to  20  per  cent.     It  can  be  reduced  by 
good  workmanship  to  about  10  per  cent,  but  cannot  be  avoided 
altogether. 

3.  To  a  series  of  imperfections  in  the  compressing  cylinders, 
such  as  insufficient  supply  of  free  air,  difficult  discharge,  defective 
cooling  arrangments,  poor  lubrication,  etc. 

4.  To  heat  generated  during  compression  which  increases  the 
power  required  for  compressing  a  given  quantity  of  air,  for  which 
there  is  no  return,  as  the  heat  is  afterward  dissipated  in  trans- 
mission. 

5.  To  loss  of  pressure  in  the  pipe  line,  due  to  friction,  etc. 

6.  To  friction  and  fall  of  temperature  during  expansion  of  the 
air  in  the  cylinder  of  the  air  engine. 

7.  To  leaks  in  the  compressor,  the  pipe  line,  and  in  the  air 
engine. 

Example.— Let  us  follow  a  volume  of  10  cu.  ft.  of  free  air,  having  an 
initial  temperature  of  60°  Fahr.,  from  the  moment  it  is  taken  into  the 
cylinder  of  the  compressor  until  it  is  exhausted  from  the  air  engine. 
124 


EFFICIENCY  OF  A  COMPRESSED-AIR  SYSTEM          125 

Referring  to  the  example  under  Article  87,  we  found  that  it  took  55,600 
ft.-lb.  of  work  to  compress  these  10  cu.  ft.  of  free  air  in  one  stage  to  70 
Ib.  gage,  and  that  we  finally  deliver  into  the  pipe  line  a  volume  of  2.68 
cu.  ft.  of  air  having  an  absolute  pressure  of  50  Ib.  and  a  temperature  of 
60°  Fahr. 

Assuming  that  the  pipe  line  is  so  dimensioned  that  the  loss  of  pres- 
sure is  5  Ib.,  then  the  compressed  air  which  is  delivered  at  the  end  of 
the  pipe  line  has  an  absolute  pressure  of  45  Ib.  and  its  volume  has  ex- 
panded at  constant  temperature  to 

F2=F,p'  =  2.68  *j°  =  2.98  cu.  ft. 

f  2  4O 

According  to  equation  (1)  in  Article  113,  a  volume  of  2.98  cu.  ft.  of  air 
at  45  Ib.  absolute  if  admitted  to  and  allowed  to  expand  adiabatically 
down  to  say,  16.5  Ib.  absolute  in  an  air  engine,  is  capable  of  doing  use- 
ful work  (theoretically)  to  the  amount  of: 


Wn=  144 


[P2V2  +^^iL1_p0F1]  foot-pounds 


in  which  P2  =  45  Ib.  per  square  inch 
V2  =  2.98  cu.  ft. 
PI  =  16.5  Ib.  per  square  inch 

Vi  =  V2  ^2Yn=6.08cu.  ft. 

P«  =  14.7  Ib.  per  square  inch 
n  =  1.406 

W,  =  144   [45X2.98+J5X2'98-410665X6^-14.7X6.08] 
=  18,400  ft.-lbs. 

Deducting  15  per  cent,  for  friction,  etc.,  gives: 

Work    performed    by  air  engine,  15,600  ft.-lb. 
Work  of  compression  and  delivery,  56,600  ft.-lb. 

Efficiency  of  whole  system  =       '       =  28  per  cent. 
oOjbiHJ 

Practical  tests  frequently  show  lower  efficiencies  than  those  obtained 
by  calculation,  due  to  leaks  in  compressor,  pipe  line,  air  engine,  and  to 
other  imperfections.  If  air  is  used  in  the  motor  at  full  pressure  during 
the  entire  stroke  as,  for  instance,  in  air  drills  (see  Article  109),  the 
efficiency  sinks  to  its  lowest  level. 

As  has  been  pointed  out,  the  use  of  compound  compressors  with 
adequate  cooling  devices  and  the  use  of  higher  initial  pressures  will 
result  in  higher  mechanical  efficiency  of  the  whole  system.  One  of  the 
means  employed  at  present  to  increase  this  efficiency  is  a  system  known 
as  "Reheating"  which  is  described  under  Article  122. 


CHAPTER  XVI 
REHEATING  OF  COMPRESSED  AIR 

122.  In  preceding  articles  it  has  been  shown  that  the  available 
energy  residing  in  a  given  weight  of  compressed  air  at  the  end 
of  the  pipe  line  is  considerably  less  than  that  which  the  same 
weight  of  compressed  air  could  develop  immediately  after  leaving 
the  compressor.  This  is  due  to  the  fact  that  the  volume  of  a 
given  weight  of  air,  having  a  given  pressure,  is  smaller  at  the 
lower  temperature  which  prevails  at  the  end  of  the  pipe  line  than 
that  which  it  occupies  when  leaving  the  compressor  at  a  high 
temperature,  and  to  the  fact  that  the  available  power  residing  in 
compressed  air  is  dependent  on  volume  as  well  as  on  pressure. 

This  has  led  to  the  introduction  of  a  process  known  as  "Reheat- 
ing." By  this  process  the  volume  of  the  compressed  air  at  the 
terminal  may  be,  by  heating,  increased  so  as  to  partly  or  com- 
pletely make  up  for  loss  of  power  in  transmission. 

To  accomplish  this  result  there  must  be  an  expenditure  of  fuel. 
This  expense,  however,  is  very  light.  For  the  average  air  engine 
it  amounts  to  about  one-seventh  of  the  fuel  that  would  be 
originally  required  to  compress  air  so  that  it  would  be  in  a  condi- 
tion to  develop  an  equal  power,  it  being  assumed  that  coal  is  the 
fuel  used.  This  is  due  to  the  fact  that  the  average  efficiency  of  a 
Corliss  steam  engine  does  not  exceed  10  per  cent.,  based  on  the 
total  heat  value  of  the  fuel,  whereas  in  reheating  in  a  proper 
heater  70  per  cent,  of  the  heat  value  of  the  fuel  may  be  utilized. 
The  increase  in  efficiency  resulting  from  reheating  makes  it 
possible  to  use  a  much  smaller  air  compressor  for  performing  a 
given  amount  of  work. 

In  addition  to  increasing  the  efficiency,  the  reheating  of  com- 
pressed air  also  prevents  the  freezing  of  the  exhaust  ports  of  air 
engines  which  often  becomes  troublesome  when  air  containing 
considerable  moisture  is  exhausted  at  temperatures  below  the 
freezing  point. 

Let  us  assume  that  at  the  end  of  the  pipe  line  we  have  1  cu.  ft. 
of  air  at  75  Ib.  gage,  and  at  a  temperature  of  60°  Fahr.  and  that 
we  wish  to  double  this  volume  by  reheating. 
126 


REHEATING  OF  COMPRESSED  AIR  127 

The  volume  of  free  air  which  must  be  compressed  to  make, 
after  being  cooled  down  to  60°  Fahr.,  1  cu.  ft.  of  air  at  75  Ib.  gage, 
we  find  from  the  equation 


on  y 

whence  V  =  1  X  ~^  =  6.10  cu.  ft. 

To  compress  adiabatically  in  one  stage  6.10  cu.  ft.  of  air  to  75  Ib. 
gage  and  deliver  it  into  the  receiver  or  the  pipe  line  requires 
work  to  the  amount  of 


^)   n  -l]  foot-pounds  (theoretical) 


Adding  15  per  cent,  for  friction  we  have 
Wn  =  35,457  ft.-lb. 

If  the  compression  is  to  be  accomplished  by  a  steam  engine  cut- 
ting off  at  1/4  stroke  the  number  of  cubic  feet  of  75  Ib.  steam  re- 
quired to  do  the  work  is  found  as  follows: 


•in  which,    Wn  =  work  in  foot-pounds  =  35,457 

Pm   =  mean  effective  steam  pressure  in  pounds  per 

square  inch  =  37.8 

Vi    =  volume  of  steam  in  cubic  feet  after  expansion 
=  four  times  the  volume  we  wish  to  ascertain. 

Introducing  values     35,457  =  144  X37.8Fi 

35,457 
whence  Fl=  144X37.8  =6'52 

A  P\*7 

Dividing  by  4  —  r  —  =  1.63 

1     AQ 

Adding  15  per  cent.          1.63  -r-^-X  15  =  1.87  cu.  ft.  of  75  Ib. 

steam,  or  practically  2  cu.  ft. 

In  other  words,  to  compress  a  certain  mass  of  air  by  steam  pres- 
sure so  as  to  furnish  1  cu.  ft.  of  compressed  air  at  75  Ib.  gage  and 


128  COMPRESSED  AIR 

at  60°  Fahr.,  requires  practically  2  cu.  ft.  of  steam  at  75  Ib.  Now, 
1  cu.  ft.  of  steam  at  75  Ib.  weighs  ^^  =  0.206  Ib.  (Kinealy  steam 

engine).  Total  heat  required  to  make  1  Ib.  of  steam  at  75  Ib. 
from  water  having  a  temperature  of  60°  Fahr.,  is: 

1179- (60-32)  =  1151  B.T.U.'s  (Kinealy). 
Total  heat  required  to  make  2  cu.  ft.  of  75  Ib.  steam,  is: 
2X1151X0.206  =  474  B.T.U.'s 

From  this  it  follows  that  the  number  of  heat  units  required  to 
produce  by  steam  energy  1  cu.  ft.  of  air  at  75  Ib.  gage  and  at  60° 
Fahr.  is  474  B.T.U.'s. 

The  temperature  of  1  cu.  ft.  of  air  at  the  end  of  the  pipe  line  is 
(60+461)  =521  degrees  absolute.  To  double  the  volume  at 
constant  pressure,  we  must  double  the  temperature,  that  is,  the 
absolute  temperature  of  the  2  cu.  ft.  of  air  at  75  Ib.  gage  would 
be  1042  degrees  and  the  increase  in  temperature  is 

1042-521  =  521  degrees. 

The  weight  of  1  cu.  ft.  of  air  at  75  Ib.  gage  and  at  60°  Fahr.  is 
from  Article  24: 

F2  =  2.7077^ 
^  =  2-7077^^  =  0.466  Ib. 

The  specific  heat  of  air  at  constant  pressure  is  0.2375.  There- 
fore, to  raise  the  temperature  of  0.466  Ib.  of  air  at  constant  pres- 
sure by  521  degrees  requires 

0.466X0.2375X521=58  B.T.U.'s 

This  shows  that  to  produce  an  extra  cubic  foot  of  air  at  75  Ib. 
by  a  steam-driven  compressor  would  require  474  heat  units, 
whereas  by  reheating  we  have  at  an  expenditure  of  only  58  heat 
units  made  2  cu.  ft.  out  of  the  original  1  cu.  ft.  of  compressed  air. 

The  additional  power  cost  of  reheating,  expressed  in  heat  units, 
in  this  case  is  therefore  only  one-eighth  of  that  of  compression  by 
steam  energy. 

In  practice,  no  attempt  is  made  to  double  the  volume  of  com- 
pressed air,  after  it  arrives  at  the  air  engine,  because  at  tempera- 


REHEATING  OF  COMPRESSED  AIR 


129 


tures  much  above  300°  Fahr.  the  lubricant  in  the  motor  is  apt  to 
charr,  causing  severe  cutting  action  on  the  valves,  rods,  and 
stuffing  boxes. 

To  increase  the  volume  of  the  compressed  air  by  reheating 
from  40  to  50  per  cent,  is  considered  quite  satisfactory.  Beyond 
that,  the  air  is  heated  only  sufficiently  to  compensate  for  heat  loss 
during  its  passage  from  the  heater  to  the  air  engine.  To  minimize 
this  loss,  the  heater  should  be  placed  as  near  the  point  of  use  as 
circumstances  will  permit,  and  the  pipe  between  the  heater  and 
the  machine  should  be  well  covered. 


FIG.  19.— Sullivan  Air  Reheater. 

In  the  following  articles  are  illustrated  and  described  two  types 
of  reheaters  which  are  being  used  in  operations  where  compressed 
air  is  employed  for  power  purposes. 

AIR  REHEATERS 

123.  The  Sullivan  air  reheater,  illustrated  in  Fig.  19,  consists 
of  a  series  of  hollow  annular  rings,  forming  the  heating  surface, 


130 


COMPRESSED  AIR 


REHEATING  OF  COMPRESSED  AIR  131 

surrounded  by  asbestos  matting  and  enclosed  in  a  sheet-steel 
shell.  The  rings  and  shell  rest  upon  two  cast-iron  rings,  lined 
with  fire  brick,  forming  the  fire  box.  The  latter  is  provided  with 
dumping  grate  and  doors  as  shown.  The  hot  gases  after  cir- 
culating around  the  rings,  escape  through  the  hood  and  smoke 
pipe  on  top. 

Air  enters  the  reheater  at  the  top  and  is  forced  to  take  a  cir- 
cuitous passage  through  the  annular  rings  by  means  of  baffle 
plates  so  that  it  comes  in  contact  with  the  heating  surface.  The 
heated  sections  are  designed  so  as  to  prevent  leakage  in  the 
joints,  due  to  expansion.  The  heated  air  leaves  the  reheater  by 
a  flanged  opening  in  the  bottom  ring,  similar  to  that  by  which  it 
enters  the  top  ring. 

These  reheaters  are  designed  for  burning  coal,  but  may  be 
adapted  for  oil  fuel. 

124.  The  Sergeant  air  reheater,  made  by  the  Ingersoll-Rand 
company,  is  shown  in  Fig.  20.     The  air  enters  at  the  top  of  the 
heater,  is  forced  in  thin  sheets  through  the  annular  space  between 
the  inner  shell  (A)  and  outer  shell  (B)  of  the  heater,  and  leaves 
the  latter  at  the  bottom.     The  increased  air  space  between  in- 
take and  discharge  pipes,  due  to  the  conical  shape  of  the  castings, 
provides  for  the  expansion  of  the  air  in  heating.     The  outer  shell 
is   surrounded   by   a  mantel  (C)   of  sheet  iron  and  the  space 
between  the  latter  and  the  shell  (B)  is  packed  with  asbestos. 

125.  Other  reheaters,  using  steam,  are  successfully  employed 
for  surface  work.     Those  described  are,  in  general,  not  suitable 
for  underground  work  in  mining  operations  where  the  smoke 
from  coal  or  oil  fuel  is  objectionable.     Although  a  number  of 
appliances  have  been  tried  for  such  work,  no  heater  that  could  be 
used  satisfactorily  under  all  conditions  has  made  its  appearance 
as  yet. 


PART  IV 

AIR  COMPRESSORS  AND  ACCESSORIES 
CHAPTER  XVII 

EXAMPLES  OF  MODERN  AIR-COMPRESSORS  OF  THE 
RECIPROCATING  TYPE 

126.  In  the  following  articles  a  few  prominent  types  of  com- 
pressors, selected  at  random,  are  illustrated  and  described  for  the 
purpose  of  demonstrating  the  practical  application  of  the  theo- 
retical principles  discussed  in  preceding  chapters. 

The  design  and  construction  of  compressors  is  a  subject  of 
mechanical  engineering.  No  attempt  has  been  made  here  to 
treat  this  subject  in  detail.  But  the  writer  believes  that  a  few 
general  remarks  on  the  construction  of  modern  compressors  will 
prove  helpful  to  the  engineer  in  making  a  judicious  selection  of 
machines,  when  called  upon  to  install  a  compressed-air  plant. 

127.  Fig.  21  gives  plan  and  elevation  of  five  types  of  steam- 
driven  compressors,  showing  some,  but  by  no  means  all  the 
possible  combinations  of  steam  and  air  cylinders.     Compressor 
builders,  as  a  rule,  designate  them  either  as  "straight-line"  or 
"duplex"  compressors. 

OPERATION  OF  STEAM-DRIVEN,  STRAIGHT -LINE  COMPRESSORS 

128.  If  we  study  the  section  of  the  steam  and  air  cylinders  of 
a  compressor  as  shown  in  Fig.  22  and  assume  the  piston  to  move 
in  the  direction  of  the  arrow,  we  note  the  following  conditions: 

In  the  air  cylinder,  at  the  beginning  of  the  stroke  the  resistance 
to  the  advance  of  the  piston  is  practically  zero.  The  pressure, 
however,  begins  to  rise  at  once,  steadily  increasing  the  corre- 
sponding resistance  against  the  piston  until  close  to  the  end  of 
the  stroke  at  A  the  receiver  pressure  is  reached,  when  the  dis- 
charge valves  open.  From  this  point  to  the  end  of  the  cylinder 
at  B  the  piston  travels  against  a  practically  uniform  maximum 
pressure  in  delivering  the  air  into  the  receiver. 

On  the  return  stroke,  the  compressor  being  double-acting,  the 
resistance  is  again  zero  at  the  beginning  of  the  stroke  and  maxi- 
mum for  the  latter  part  of  it. 

132 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     133 


In  the  steam  cylinder  the  development  of  power  is  precisely  the 
reverse  of  the  distribution  of  resistance  in  the  air  cylinder. 

Here  the  pressure  is  maximum  at  the  beginning  of  the  stroke 
and  practically  uniform  until  cut-off  occurs  at  D.  Then  the 


STRAIGHT   LINE 

PLE    AIR  SIMPLE    STE 


DUPLEX  Q 

SIMPLE   STEAM  SIMPLE    AIR  SIMPLE    STEAM  COMPOUND    AIR 


COMPOUND    STEAM  COMPOUND   AIR 


DIAGRAM 

SHOWING 

OUTLINE   ELEVATION  AND  PLAN 
OF  FAMILIAR  TYPES 
OF  STEAM-DRIVEN 

AIR  COMPRESSORS 


FIG.  21. 

pressure  rapidly  falls  all  the  way  to  the  end;  so  that  in  any 
compressor  of  the  straight-line  type  the  steam  power  is  in  excess 
of  the  work  to  be  done  at  the  beginning  of  the  stroke  in  either 
direction  and  inadequate  to  overcome  the  resistance  of  the  air  at 
the  other  end  of  the  stroke,  except  with  the  assistance  of  fly- 
wheels. 


134 


COMPRESSED  AIR 
C   D 


A     B 


4^—1 

V! 

>. 

/     i 

) 

^ 

STEAM 

AIR 

FIG.  22. 

FIG.  23.— Sullivan    Straight-line    Steam-driven  Single-stage  Compressor. 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     135 

The  excess  pressure  at  the  beginning  of  the  stroke  causes  the 
fly-wheels  to  acquire  momentum  which  they  give  off  at  the 
end  of  the  stroke  to  overcome  the  excess  of  the  air-piston 
resistance. 

This  unequal  application  of  power  to  resistance  prevents 
smooth  running  in  this  class  of  compressors  and  causes  severe 
strains  in  the  moving  parts. 

129.  Type   (1).    Straight-line,     Steam-driven,     Single-stage 
Compressor. — Fig.  23  illustrates  a  compressor  of  this  type,  built  « 
by  the  Sullivan  Machinery  Company.     These  machines  have  one 
steam  and  one  air  cylinder,  set  tandem  on  a  common  piston  rod, 
and  two  fly-wheels,  usually  driven  by  outside  connecting  rods 
from  a  cross-head,  which  slides  between  guide  plates  connecting 
the  steam  and  air  cylinders.     They  are  built  and  used  for  pres- 
sures up  to  90  Ib. 

A dvantages.— Compressors  of  this  type  are  self-contained,  sim- 
ple in  construction,  strong  and  compact,  and  of  moderate  price. 
Compared  with  duplex  machines  of  equal  capacity  they  occupy  a 
smaller  floor  space  and  do  not  require  as  expensive  foundations 
as  the  latter. 

Disadvantages. — When  running  below  a  certain  speed,  most 
straight-line  compressors  have  a  tendency  to  stick  on  centers. 
Hence  an  early  cut-off  in  the  steam  cylinder  is  not  possible. 
Such  compressors  usually  run  with  5/8  to  3/4  cut-off,  resulting 
in  high-steam  consumption,  averaging  from  40  to  50  Ib.  per  horse- 
power hour. 

130.  Type  (2).     Straight-line,  Steam-driven,  Two-stage  Com- 
pressor.— Fig.  24  illustrates  a  machine  of  this  type,  built  by  the 
Sullivan  Machinery  Company.     These  machines  have  one  steam 
and  two  air   cylinders,   set  tandem  on  a  common  piston  rod. 
The  air  is  compressed  in  the  larger  (low-pressure)  cylinder  to  an 
intermediate  pressure,  whence  it  passes  by  way  of  an  inter-cooler 
into  the  smaller  (high-pressure)  cylinder,  where  it  is  compressed 
to  the  final  pressure. 

Advantages.- — If  properly  designed  and  cared  for,  these  machines 
have  the  advantages  pertaining  to  compound  compression  as 
pointed  out  under  Article  75. 

Disadvantages. — In  addition  to  the  disadvantages  pointed  out 
for  Type  (1),  which  apply  to  all  straight-line  compressors,  the 
compounding  of  the  air  cylinders  complicates  the  machine, 
increases  the  relative  cost  of  it  for  the  work  it  does,  makes  all 


136 


COMPRESSED  AIR 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     137 


138 


COMPRESSED  AIR 


parts  less  accessible  for  adjustment,  while  it  has  left  the  machine 
with  its  usual  inability  to  run  at  slow  speed. 

131.  Operation  of  Steam-driven,  Duplex  Compressors. — A 
duplex  air  compressor  is,  in  essential  effect,  a  combination  of 
two  straight-line  machines,  so  far  as  the  steam  and  the  air  cylin- 
ders are  concerned,  with  a  single  crank  shaft  and  a  single  fly- 
wheel serving  both,  there  being  a  single  connecting  rod  for  each 
side  and  a  single  crank  on  each  end  of  the  shaft. 

In  the  duplex  compressor  the  operating  conditions  are  in 
decided  contrast  to  those  described  for  the  straight-line  com- 
pressors. 

Quartering  Cranks. — The  first  special  feature  of  advantage  of 
the  duplex  machine  is  in  the  arrangement  of  the  cranks  in  relation 
to  each  other  upon  the  ends  of  the  shaft.  These  are  set  with 
one  of  the  cranks  a  quarter  of  a  circle  in  advance  of  the  other, 
the  result  of  which  is  to  so  time  the  movements  of  the  pistons  on 
the  two  sides  of  the  machine  that  one  will  be  at  nearly  midstroke 
when  the  other  is  at  the  beginning  or  end  of  its  stroke.  The  two 
sides  thus  alternately  help  each  other  over  the  hard  places,  and, 
while  not  under  nearly  as  great  obligation  to  the  fly-wheel,  their 


FIG.  25. 

action  is  much  steadier  and  so  free  from  excesses  of  pressure  over 
resistance  or  of  resistance  over  pressure,  that  the  rotation  is  more 
uniform.  The  practical  limit  of  speed  is  lowered  to  perhaps 
one-quarter  of  the  lowest  speed  permissible  in  the  straight-line 
type,  so  that,  if  the  cut-off  on  the  steam  cylinder  is  properly  set, 
the  machine  may  be  made  to  automatically  stop  and  start  itself 
and  to  run  at  any  speed  down  to  the  lowest,  as  the  air  consump- 
tion may  require.  Waste  of  power  and  steam,  consequent  upon 
the  necessity  of  running  at  high  speed  to  prevent  centering, 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     139 

will  be  avoided.  The  conditions  of  pressure  and  resistance  are 
illustrated  graphically  in  the  diagram  Fig.  25. 

The  two  steam  and  air  cylinders  of  the  compressor  are  shown 
in  the  diagram  one  above  the  other.  In  the  two  upper  cylinders 
minimum  power  in  the  steam  cylinder  is  being  applied  to  maxi- 
mum resistance  in  the  air  cylinder  at  the  end  of  the  stroke.  In 
the  two  lower  cylinders  excess  power  is  being  applied  to  small 
resistance  at  midstroke,  the  surplus  pressure  acting  to  carry  the 
compressor  past  the  center  of  the  upper  cylinders. 

Similar  conditions  can  be  shown  for  other  positions  of  the 
pistons. 

131a.  Compared  with  straight-line  machines,  duplex  compres- 
sors offer  several  disadvantages  which  should  be  taken  into  con- 
sideration when  planning  an  installation. 


FIG.  26.- 


-Laidlaw-Dunn-Gordon  Duplex,  Steam-driven,  Single-stage 
Compressor. 


For  any  given  output  of  air  they  are  more  expensive  in  first  cost 
and  up-keep,  for  there  is  double  the  machinery.  There  are  double 
the  chances  of  delays,  for  either  side  may  be  necessarily  stopped 
and  then  all  the  air  is  shut  off  until  adjustments  can  be  made  to 
both  machines.  A  heated  journal  on  either  side  will  stop  both. 
The  friction  of  the  duplex  machines  exceeds  on  an  average  by 
about  5  per  cent,  the  friction  of  two  machines  working  separately. 

All  duplex  compressors  occupy  much  more  floor  space  than 
straight-line  machines  of  the  same  capacity,  consequently  require 
larger  and  more  costly  buildings  and  foundations. 

132.  Type  (3).  Duplex,  Steam-driven,  Single-stage  Com- 
pressor.— Fig.  26  shows  a  machine  of  this  type,  built  by  the 


140 


COMPRESSED  AIR 


FIG.  27. — Ingersoll-Rand  Duplex  Steam-driven  Two-stage  Compressor. 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     141 

Laidlaw-Dunn-Gordon  Co.  It  is  merely  a  combination  of  two 
straight-line,  single-stage  compressors  of  type  (1),  set  on  the  same 
shaft  with  one  fly-wheel  instead  of  two. 

It  combines  all  the  advantages  and  disadvantages  of  a  duplex 
compressor,  pointed  out  in  Articles  131  and  131a.  Compared 
with  types  4  and  5,  it  has  the  advantage  that,  if  necessary,  one 
side  can  be  operated  as  a  complete  machine. 

133.  Type  (4).     Duplex,  Steam-driven,  Two-stage  Compres- 
sor.— Fig.  27  illustrates  a  compressor  of  this  type  built  by  the 
Ingersoll-Rand   Co.     It  has  simple  steam  cylinders  and  cross- 
compound  air  cylinders.     The  inlet  valves  of  both  the  low-  and 
high-pressure  air  cylinders  are  of  the  Corliss  type.     The  inter- 
cooler  is  placed  in  the  cast-iron  frame,  which  makes  the  com- 
pressor more  compact. 

Compressors  of  this  type  partake  of  all  the  advantages  and  dis- 
advantages of  the  duplex  feature  as  well  as  of  stage-compression, 
as  pointed  out  in  Article  75.  One  objection  to  cross-compound 
air  cylinders  in  duplex  machines  is  that  under  no  circumstances 
can  one  side  be  operated  as  a  complete  machine. 

134.  Type    (5).    Duplex,    Steam-driven,    Two-stage    Com- 
pressor.— Fig.  28  illustrates  a  compressor  of  this  type,  built  by 
the  Allis-Chalmers  Company,  with  the  inter-cooler  removed. 
Both  air  and  steam  cylinders  are  cross-compound.     Inlet  valves 
are  of  the  Corliss  type.     It  is  not  possible  to  operate  one  side 
of  this  compressor  as  a  complete  machine,  on  account  of  the  cross- 
compound  feature,  which  requires  the  operation  of  both  sides 
at  the  same  time. 

135.  Other  Types  of  Steam-driven  Compressors. — For  illus- 
tration of  other  types  and  combinations  of  steam-driven,  single- 
and  multi-stage  compressors,  the  reader  is  referred  to  the  cata- 
logues and  bulletins  of  manufacturers  which,  besides   copious 
illustrations,  usually  contain  a  large  amount  of  useful  data  on  air 
compression.     The  remarks  contained  in  the  preceding  articles 
should  enable  the  reader  to  draw  fairly  correct  conclusions  as  to 
the  merits  of  the  one  or  the  other  type  and  make  of  compressor 
when  referred  to  the  needs  of  any  contemplated  installation. 

POWER-DRIVEN  AIR  COMPRESSORS 

136.  A  large  class  of  compressors  used  in  the  various  industries, 
are  of  the  power-driven  types.     That  is,  they  consist  of  one  or 
more  air  cylinders,  the  piston  rod  of  which  is  connected  through 


142 


COMPRESSED  AIR 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     143 


144 


COMPRESSED  AIR 


a  connecting  rod  and  crank  to  a  revolving  shaft,  the  latter  being 
driven  from  a  central  power  plant,  or  by  a  water-wheel,  or  by  an 
electric  motor. 

In  selecting  a  power-driven  compressor,  it  must  be  borne  in 
mind  that  it  cannot  be  hurried,  neither  can  it  be  run  at  a  speed 
little  less  than  the  maximum.  Steam-driven  machines  can  be 
run  at  variable  speed  to  suit  the  requirements,  but  the  power- 
driven  compressor  must  always  run  at  full  speed,  and  variations 
of  demand  can  only  be  met  by  unloading,  either  wholly  or  in  part 
as  circumstances  may  require. 

For  unloading  devices  see  Articles  156-160. 

Compressors  of  small  power  can  be  driven  by  belts,  chains  or 
gears.  Moderately  large  powers,  unless  driven  direct,  are  depend- 
ent upon  ropes  or  belts,  while  for  compressors  of  very  large 
capacity  direct  drive  seems  the  most  satisfactory. 


BELTED,  COMPARED  WITH  DIRECT  STEAM  POWER 
COMPRESSORS 

137.  The  question  is  frequently  asked:  Under  what  conditions 
is  a  belted  compressor  more  advisable  than  one  having  its  own 
independent  steam  engine?  In  an  establishment  having  a  large 
high-class  main  engine  of  abundant  power,  the  belt  pattern  offers 
the  advantage  of  compressing  the  air  with  the  same  steam  econ- 


FIG.  30.— Norwalk  Two-stage  Compressor  with  Water-wheel  Drive. 

omy  as  is  obtained  in  the  large  steam  engine,  and  will  therefore 
prove  more  economical  in  first  cost  as  well  as  in  operation. 
Economy,  however,  must  always  be  studied  not  in  the  engine 
alone,  but  in  the  compressor  as  well  and  when  the  air  demands 
are  of  considerable  relative  consequence,  the  power  required  may 
necessitate  the  individual  engine  for  the  compressor. 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     145 

138.  Fig.  29  illustrates  a  two-stage  compressor  of  the  belt 
pattern,  built  by  the  Norwalk  Iron  Company.     The  large  band 
wheel  serves  for  a  driving  pulley  as  well  as  for  a  fly-wheel  and  can 
be  belted  to  the  pulley  on  a  large  main  drive  shaft  or  to  the  pulley 
of  an  electric  motor. 

139.  Compressors  with  Direct  Water-wheel  Drive. — Fig.  30 
illustrates  a  compressor  of  this  type  built  by  the  Norwalk  Iron 
Company.     For  the  band  wheel  a  heavy  fly-wheel  is  substituted 
and  on  this  the  water-wheel  buckets  are  mounted. 

Where   abundant  water  power  is   available  for   continuous 
service  such  compressors  may  be  used  to  great  advantage. 

ELECTRICALLY  OPERATED  COMPRESSORS 

140.  Like  all  power-driven  compressors,  electrically  operated 
compressors  must  be  run  at  constant  speed  and  must  therefore 


FIG.  31. — Ingersoll-Sergeant  Rope-driven  Compressor. 

be  provided  with  unloading  devices  to  regulate  the  output,  whe 
used  for  intermittent  demand. 


146 


COMPPESSED  AIP 


FIG.  32. — Nordberg  Electrically-driven  Geared  Two-stage  Compressor  of 
the  Duplex  Type. 


Fia.  33.— Ingersoll-Rand  Direct-connected   Electrically-driven   Two-stage 
Compressor. 


AIR-COMPRESSORS  OF  THE  RECIPROCATING  TYPE     147 

Besides  belt  or  rope  driven,  in  which  the  pulley  of  the  motor  is 
connected  by  belt  or  ropes  with  the  band  wheel  of  the  compressor, 
as  shown  in  Fig.  31,  electric  motors  are  also  geared  or  direct  con- 
nected to  the  revolving  shaft  of  the  compressor. 

141.  Fig.   32  illustrates  an   electrically  driven,  geared,  two- 
stage  compressor  of  the  duplex  type,   built  by  the  Nordberg 
Mfg.  Co.     The  inlet  valves  which  are  of  the  Corliss  type  are 
released  by  an  unloading  device  from  the  operating  mechanism, 
when  they  are  wide  open  and  are  kept  in  that  position  until  more 
air  is  required.     The  releasing  is  effected  by  cams,  operated  by  a 
frictionless  plunger  on  which  the  air  pressure  acts  in  opposition 
to  a  weight.     These  cams  throw  out  a  latch  so  placed  on  the  valve 
operating  lever,  that  it  closes  the  valve,  while  the  opening  is 
effected  by  a  projection  acting  on  the  valve  operating  lever. 
The  cams  are  so  adjusted  that  first  one  and  then  the  other 
engages  the  releasing  latch. 

142.  Fig.  33  illustrates  a  direct-connected,  electrically  driven, 
two-stage  compressor,  built  by  the  Ingersoll-Rand  Company. 


CHAPTER  XVIII 
IMPORTANT  MECHANICAL  FEATURES  OF  AIR  COMPRESSORS 

143.  Without  going  into  detail  of  construction,  attention  will 
be  called  to  some  of  the  mechanical  features  which  influence  the 
operation  of  a  compressor  to  such  an  extent  that  unsatisfactory 
results  can  in  most  cases  be  traced  to  either  defective  construction 
or  to  neglect  of  proper  care  of  certain  parts  of  the  machine.     A 
proper  understanding  of  their  function  will  enable  the  operator 
to  trace  to  the  most  probable  source,  any  failure  of  the  compressor 
to  do  its  duty,  and  to  apply  the  necessary  remedies,  if  such  failure 
is  not  due  to  inherent  imperfections  of  the  machine  itself. 

INLET  VALVES 

144.  The  inlet  valves  of  a  compressor  are  either  of  the  poppet 
type,  being  held  to  their  seats  by  springs,  or  they  are  mechanically 
moved,  resembling  in  their  general  form  and  operation  the  steam 
valves  of  a  Corliss  engine. 

145.  Poppet  Inlet  Valves. — All  poppet  valves,  whether  used  as 
inlet  or  discharge  valves,  consist  essentially  of  three  main  parts: 
a  valve  proper,  a  valve  guide  and  a  spring.     For  illustration 
see  Fig.  36. 

In  general,  poppet  inlet  valves  are  open  to  the  objection  that, 
inasmuch  as  the  springs  must  insure  prompt  closing  at  all  speeds, 
they  must  have  considerable  strength.  This  causes  throttling 
of  the  inlet  and  hence  loss  of  volumetric  efficiency  and  requires 
extra  power  to  make  up  for  this  loss. 

Another  objection  is,  that  the  incoming  air  passes  in  a  very 
thin  stream  over  these  heated  surfaces  and  is  itself  heated  and 
rarefied  as  a  consequence.  The  undesirable  effects  of  these 
conditions  have  been  pointed  out  under  Articles  54  and  87. 

These  objections  have  led  to  the  introduction  of  inlet  valves 
of  the  Corliss  type. 

146.  Inlet  Valves  of  the  Corliss  Type.— Fig.  34  illustrates  the 
construction  of  an  air  inlet  valve  of  the  Corliss  type,  employed 
in  some  of  the  Ingersoll-Rand  compressors.     (See  Fig.  27.) 

148 


MECHANICAL  FEATURES  OF  AIR  COMPRESSORS       149 

The  valve  is  made  of  cast  iron  and  is  operated  by  a  steel  stem 
"A,"  which  has  a  large  flange  "B"  provided  with  a  series  of 
tongues  on  its  inner  face,  machined  to  match  with  grooves  on 
end  of  valve  "C."  Valve  bonnet  "D"  is  of  the  stufferless  type, 
the  stem  being  made  self  packing  by  means  of  a  fiber  washer  "E." 
Contact  is  maintained  between  faces  of  fiber  washer  and  face  of 
valve  stem  collar,  also  bonnet  face,  by  means  of  a  spring  and 
thimble  "F"  in  back  bonnet  "G."  Lubrication  for  the  valve 
is  provided  for  at  "H"  and  "I." 

Valves  of  the  Corliss  type  are  positively  moved  from  the  main 
shaft  of  the  compressor  as  shown,  for  instance,  on  the  compressor 
illustrated  in  Fig.  28. 


FIG.  34.— Air  Valve  of  the  Corliss  Type. 

The  large  port  of  these  valves  and  their  positive  operation 
insures  an  air  supply  that  keeps  pace  with  the  speed  of  the 
machine. 

147.  Ingersoll-Rogler  Valve.— The  valve  illustrated  in  Fig. 
35  is  of  the  disc  type.  It  consists  essentially  of  a  valve  seat 
(A),  cast  with  circular  ports,  which  supports  valve  (F)  and 
cushion  plate  (H)  that  are  separated  from  each  other  by  washers 
(E  and  G}.  All  are  held  together  by  valve  bolt  (B}.  Portions 
(Af)  of  valve  (F}  are  elastic  spring  arms  that  hold  the  valve 
absolutely  in  one  position  and  always  seat  it  in  the  same  place. 
The  four  spring  arms  of  cushion  plate  (H)  hold  the  valve  on 
its  seat  against  a  slight  tension  of  the  integral  valve  arms  (M). 
As  soon  as  the  proper  air  pressure  is  reached,  the  valve  opens 
against  these  springs  and  closes  again  at  the  instant  the  piston 
starts  on  its  return  stroke. 

Owing  to  the  light  weight  and  low  lift,  the  valve  is  subject 
to  little  wear  and  shock.  The  time  required  to  open  and  close 
it  being  very  brief,  higher  speeds  and  therefore  greater  capacity 
are  possible  than  would  be  safe  with  other  types  of  valves. 


150 


COMPRESSED  AIR 


The  absence  of  gears  for  operating  the  valve  eliminates  friction 
and  since  there  are  no  rubbing  parts,  the  valve  needs  no  lubrication. 


FIG.  35. — Section  Showing  Inlet  Valve  in  the  Air  Cylinder  of  a  Modern 
Ingersoll-Rand  Compressor. 


DISCHARGE  VALVES 

148.  Discharge   valves,   like  inlet   valves,   are  either  of   the 
poppet  or  disc  type  or  they  are  mechanically  moved  and  of 
similar  construction  as  the  inlet  valve  shown  in  Fig.  34. 

149.  Poppet  Valves. — Fig.  36  illustrates  a  simple  construction 
of  a  poppet  discharge  valve,  used  in  some  Ingersoll-Rand  com- 
pressors.    (See  Fig.  10.) 

The  valve  proper  is  ground  to  an  accurate  seat,  while  the  cap 
or  valve-guide  is  ground  to  a  wide  guide  surface  insuring  the  re- 


MECHANICAL  FEATURES  OF  AIR  COMPRESSORS       151 

turn  of  the  valve  to  its  seat  with  precision  and  tightness.  A  small 
volume  of  air  is  compressed  between  valve  and  guide  at  the  end 
of  the  lift,  affording  a  cushion  which  removes  shock  without 
interfering  with  the  quick  action  of  the  valve.  The  valve  is  free 
to  turn  and  is  self-grinding.  The  spiral  spring  is  made  of  the 
proper  pitch  and  strength  to  return  the  valve  to  its  seat  at  the 
proper  moment. 

Discharge  valves  of  the  poppet  type  are  open  to  similar  objec- 
tions as  poppet  inlet  valves;  which  has  led  to  the  introduction  of 
mechanically  moved  valves  of  the  Corliss  and  other  types. 


FIG.  36.— Air  Valve  of  the  Poppet  Type. 

150.  Mechanically  Moved  Discharge  Valves.— When  of  the 

Corliss  type,  they  are  essentially  of  the  same  construction  and 
are  operated  in  the  same  manner  as  the  valve  illustrated  in 
Fig.  34. 

The  principal  objection  to  positively  operated  discharge  valves 
is,  that  the  point  of  opening  is  fixed  and  thus  too  late  when  the 
discharge  pressure  is  below,  or  too  early  when  above  normal 
pressure,  as  this  frequently  happens  with  compressors  supply- 
ing an  intermittent  demand.  Such  compressors,  when  using 
mechanically  controlled  discharge  valves,  have  the  latter  usually 
arranged  so  that  they  are  free  to  open  automatically,  but  are 
positively  closed. 

151.  Fig.  37  shows  such  a  valve,  employed  in  some  compressors 
built  by  the  Allis  Chalmers  Co.     As  seen,  the  inlet  valves  are  of 
the  usual  Corliss  type;  the  discharge  valves  (A)  open  as  soon  as 
the  air  pressure  in  the  cylinder  reaches  that  of  the  air  in  the 
receiver  and  are  positively  closed  by  plungers  (£),  which  are 
operated  by  being  connected  to  a  wrist  plate  driven  by  an  eccen- 


152  COMPRESSED  AIR 

trie  on  the  main  shaft.  The  movement  of  the  plunger  is  so  timed 
as  to  positively  bring  the  valves  to  their  seat  just  as  the  piston 
reaches  the  end  of  the  stroke,  thus  avoiding  any  slip  of  the  air 
back  by  the  valves.  During  the  return  stroke  of  the  piston  the 
valves  are  held  to  their  seats  by  the  discharge  air  pressure  until 
the  process  is  repeated  on  the  succeeding  forward  stroke.  In 
closing,  the  air  between  plunger  and  valve  forms  a  cushion  so 
that  the  valve  is  brought  to  its  seat  without  noise  or  pounding. 

152.  Fig.  38  shows  an  arrangement  used  in  some  compressors, 
built  by  the  Nordberg  Mfg.  Co.     Both  inlet  and  discharge  valves 


FIG.  37. — Allis-Chalmers  Discharge  Valve. 

are  of  the  Corliss  type.  In  the  center  of  each  discharge  valve  are 
fitted  a  row  of  self-acting  poppet  valves,  which  open  automatically 
when  for  any  reason  the  discharge  pressure  is  below  normal. 

153.  Corliss  valves  are  not  suited  for  discharge  valves  in  single- 
stage  compressors,  compressing  to  more  than  30  Ib.  gage,  because 
the  time  between  the  opening  and  closing  is  too  short  to  be  per- 
formed by  a  positive  mechanism.     In  such   cases  self-acting 
poppet  valves  are  used. 

They  may  be  used,  however,  in  single-,  two-  or  three-stage 
compressors,  in  which  they  have  to  be  kept  open  during  nearly 
one-half  of  the  stroke. 

THE  INTER-COOLER 

154.  Inasmuch  as  the  intercooler  is  the  principal  device  by 
which  a  saving  of  power  in  stage  compression  is  accomplished 
(see  Article  57),  it  must  be  planned  and  designed  so  as  to  cool  to 
initial  temperature  the  heated  air  that  passes  through  it  on  its 
way  from  one  cylinder  of  a  compressor  to  another. 


MECHANICAL  FEATURES  OF  AIR  COMPRESSORS       153 


To  do  this  effectively,  it  must  possess  the  following  essential 
properties: 

1.  The  cooling  surface  offered  to  the  circulating  air  must  be 


FIG.  38.— A  Nordberg  Discharge  Valve  of  the  Corliss  Type    Fitted  with 
Self-acting  Poppet  Valves. 

ample.     This  is  generally  based  on  the  quantity  of  "free  air" 
compressed  per  minute. 

2.  The  total  volume  should  be  as  large  as  possible.  two 

inter-coolers  having  the  same  amount  of  cooling  surfaces,  the 


154 


COMPRESSED  AIR 


one  of  larger  volume  offers  the  advantage  of  allowing  the  air  to 
be  in  contact  with  the  cooling  tubes  for  a  longer  period. 

3.  The  water-circulation  should  be  planned  so  as  to  make  the 
water  flow  unrestricted  and  with  proper  velocity  through  the 
pipes  and  thus  absorb  and  carry  away  the  maximum  number  of 
thermal  units  contained  in  the  air. 

4.  It  should  be  provided  with  means  for  bringing  the  air  in 
continuous  contact  with  the  cooling  surfaces.     This  is  usually 
accomplished  by  so-called  "baffle  plates." 

5.  It  should  have  convenient  appliances  for  draining  the  con- 
densed moisture,  and  should  permit  easy  access  for  inspection 
and  repairs. 


CONDENSATION  ORAIK 

FIG.  39.— Section  of  Intel-cooler. 


155.  Fig.  39  gives  a  sectional  view  of  an  inter-cooler  built  in 
accordance  with  modern  practice.  It  consists  of  a  cylindrical 
iron  shell  "A"  containing  a  nest  of  tubes  "B,"  through  which 
cold  water  is  circulated.  The  tubes  are  so  spaced  as  to  divide 
the  air  into  thin  sheets,  and  by  means  of  baffle  plates  "C,"  the 
air  is  deflected  and  brought  in  contact  with  all  parts  of  the  cooling 
surface,  before  it  leaves  the  inter-cooler.  The  tubes  are  expanded 
into  tube  sheets  "D,"  and  the  rear  tube  sheet  is  covered  by  a 
head  "E"  which  is  in  no  wise  connected  to  the  shell  but  is  free 
to  slide  within  it,  thus  providing  for  any  differences  in  expansion 
between  shell  and  tubes.  The  rear  end  of  the  shell  is  closed  by  a 
separate  head.  The  front  head  "F"  can  be  removed  and  the 
tubes  withdrawn  for  inspection  and  cleaning.  The  heads  are 
provided  on  the  inside  with  ribs,  which  abut  against  the  tube 
sheets  and  compel  the  water  to  pass  from  end  to  end  of  the  inter- 
cooler  several  times,  thus  obtaining  the  maximum  cooling  effect 
from  a  given  quantity  of  circulating  water. 


CHAPTER  XIX 
COMPRESSOR  ACCESSORIES 

156.  The  most  essential  accessories  of  a  compressor  plant  are 
automatic  regulators  and  receivers.     Only  a  few  types  of  each 
are  illustrated  and  described  in  the  following  articles.     They 
were  selected  at  random,  not  with  any  intention  of  giving  them 
preferences  over  other  designs  or  makes,  but  merely  to  demon- 
strate how  certain  demands  which  are  made  on  almost  every 
compressor  plant  may  be  filled  by  mechanical  means. 

AUTOMATIC  REGULATORS 

157.  In  the  industries  using  compressed  air,  particularly  in 
mining  operations,  the  consumption  of  air  is  often  irregular  and 
intermittent.     For  short  periods  it  may  cease  entirely. 

To  keep  on  compressing  air  when  the  demand  is  falling  off 
would  mean  a  waste  of  energy  in  that  the  surplus  air  would 
simply  blow  off  through  the  safety  valve  of  the  receiver.  To 
prevent  such  waste,  compressors  supplying  an  irregular  demand 
are  provided  with  so-called  automatic  regulators. 

Power-driven  compressors,  which  must  run  at  constant  speed, 
and  steam-driven,  straight-line  compressors  which  are  liable  to 
stick  on  centers  when  run  below  a  certain  speed,  are  usually 
provided  with  so-called  "unloaders." 

Steam-driven,  duplex  compressors  may.  use  unloaders  or  speed 
governors,  or  a  combination  of  both. 

158.  Air  Cylinder  Unloaders. — -These  devices  are  designed  to 
automatically  shut  off  the  supply  of  free  air  to  the  compressor 
when  the  consumption  decreases. 

After  shutting  off  the  in-take,  all  the  useful  work  ceases  and 
only  sufficient  energy  is  expended  to  overcome  friction  of  the 
moving  parts. 

Fig.  40  shows  an  unloading  device,  built  by  the  Union  Steam 
Pump  Co.  It  consists  of  a  casing  (a)  and  a  plunger  (6),  which 
controls  the  admission  of  air  into  the  compressor  through  the 

155 


156 


COMPRESSED  AIR 


inlet  pipe  (c).    Attached  to  one  side  of  the  casing  is  an  auxiliary 
piston  (d),  a  lever  (/)  and  a  weight  (g). 

The  air  pressure  on  the  auxiliary  piston  is  balanced  by  the 
weight  which  can  be  adjusted  to  unload  the  compressor  at  any 
desired  pressure.  When  the  decreased  demand  for  air  raises  the 
pressure  in  the  receiver  beyond  the  normal,  this  increased  pres- 
sure lifts  the  auxiliary  piston  (d),  closes  the  port  (h)  and  admits 
air  at  receiver  pressure  through  port  (m)  under  the  plunger  (6). 
The  latter  is  thus  raised  and  closes  the  air  inlet  pipe  (c). 


FIG.  40. — Air  Cylinder  Unloader. 

When  the  receiver  pressure  falls  to  normal  pressure  again,  on 
increased  demand  of  air,  piston  (d)  is  pressed  downward  by 
weight  (g),  port  (m)  is  closed,  while  the  air  confined  under  plunger 
(6)  is  exhausted  into  the  atmosphere  through  port  (/i).  Plunger 
(6)  by  its  own  weight  drops  into  its  first  position,  thus  opening 
the  main  inlet  pipe  (c)  and  allowing  the  compressor  to  resume  its 
useful  work. 

169.  Combined  Speed  Governor  and  Air-pressure  Regulator. 
• — In  mining  operations  it  happens  at  times  that  rock  drills, 
hoists,  pumps,  etc.,  using  air,  are  all  started  more  or  less  simul- 
taneously, causing  the  compressor  to  run  at  an  injurious  speed  to 
supply  the  unusual  demand.  At  other  times  the  demand  may 
sink  below  the  normal  or  cease  altogether. 


COMPRESSOR  ACCESSORIES  157 

Compressors  subject  to  such  conditions  are  usually  provided 
with  a  combined  speed  governor  and  pressure  regulator. 

160.  Fig.  41  shows  such  a  device,  furnished  with  certain  com- 
pressors of  the  Ingersoll-Rand  Co.  This  device  consists  of  a 
regular  fly-ball  governor  (a)  with  an  auxiliary  air  cylinder  (6) 
for  holding  a  constant  air  pressure  in  the  receiver.  A  casing  (c) 
contains  a  special  balanced  throttle  valve,  the  spindle  of  which  is 
connected  to  the  governor,  the  latter  being  belt-  or  chain-driven 


FIG.  41. — Ingersoll-Rand  Combined  Speed   Governor  and  Air  Receiver. 

from  the  compressor  shaft.  By  this  arrangement  the  steam 
supply  is  throttled  when  the  speed  exceeds  the  desired  limit, 
which  provides  a  safety  stop  against  "runaways"  should  an  air 
pipe  be  broken.  The  piston  in  the  air  cylinder  (6)  presses  against 
a  weighted  lever  (e).  This  cylinder  is  connected  by  a  small  pipe 
(/)  to  the  top  of  the  air  receiver.  The  inner  end  of  the  weighted 
levar  connects  with  the  spindle  (d)  of  the  balanced  throttle  valve 
throagh  a  link  which  makes  the  action  of  the  air  cylinder  (6) 
independent  of  the  governor  (a).  When  the  pressure  in  the 
receiver  exceeds  the  normal,  the  weighted  lever  (e)  is  raised  and 


158  COMPRESSED  AIR 

the  balanced  throttle  valve  closed  to  a  point  which  admits  just 
enough  steam  to  turn  the  machine  over  at  the  speed  necessary  to 
supply  a  volume  of  air  equal  to  that  drawn  from  the  receiver. 

If,  from  any  cause,  the  air  pressure  in  the  receiver  diminishes, 
the  weighted  lever  gradually  drops,  owing  to  the  decrease  of 
pressure  in  the  small  cylinder  (6).  This  action  opens  the  throttle 
admitting  more  steam  into  the  engine.  Should  an  air  pipe 
break,  or  should  too  great  a  demand  be  made  upon  the  com- 
pressor, keeping  the  air  pressure  down  so  that  the  air  piston  does 
not  perform  the  work,  the  machine  will  speed  up  to  a  point 
where  the  centrifugal  governor  partially  closes  the  throttle, 
bringing  the  engine  back  to  its  rated  full  speed  or  the  speed  for 
which  the  governor  is  set. 

AIR  RECEIVERS 

161.  Air  receivers  have  become  indispensable  accessories  of 
every  compressed-air  installation.  Since  their  design  and  size 
influence  to  a  large  extent  the  working  of  the  whole  system,  the 
principal  functions  which  they  have  to  perform  should  be  well 
understood. 

Receivers  are  used  for  three  distinct  purposes: 

1.  To  equalize  the  pulsations  of  the  air  coming  from  the  com- 
pressor intermittently  and  to  cause  it  to  flow  with  a  uniform 
velocity  into  the  pipe  line.     Unless  there  is  ample  space  for 
accommodating  the  air  coming  from  the  compressor,  the  pressure 
will  run  up  momentarily  in  excess  of  the  normal,  thus  throwing 
unnecessary  strain  on  the  machine  and  consuming  extra  power. 

Receivers  are  employed  to  provide  this  space  and  in  order  to 
perform  this  function  effectively,  they  should  be  placed  within 
a  few  feet  of  the  compressor  and  connected  with  it  by  a  pipe  of 
sufficient  size. 

2.  To  keep  the  friction  of  air  in  the  pipe  line  as  small  and  as 
uniform  as  possible,  thereby  preventing  a  loss  of  energy.     In 
Article  100  it  has  been  shown  that  friction  increases  with  velocity 
and  the  latter  increases  with  the  difference  of  pressure  at  both 
terminals  of  the  pipe  line.     It  is  therefore  important  to  keep  this 
difference  as  small  and  as  uniform  as  possible.     In  a  long  line  this 
is  best  accomplished  by  placing  another  receiver  at  the  end  of  the 
line,  close  to  the  air  engine.     Just  as  a  receiver  near  the  com- 
pressor prevents  the  rise  of  pressure  above  the  normal  when 


COMPRESSOR  ACCESSORIES 


159 


air  is  forced  into  the  pipe,  one  at  the  end  of  the  line  will  pre- 
vent a  sudden  fall  of  pressure  below  the  normal  when  air  is 
quickly  withdrawn  from  the  pipe  line. 

3.  To  collect  the  moisture  and  grease  which  the  air  carries  in 
suspension  and  which  would  otherwise  be  carried  into  the  pipe  line 
by  the  force  of  the  current.  By  allowing  the  heated  air  to  pause 
in  its  flow  through  the  receiver,  it  is  cooled  and  will  therefore  drop 
most  of  the  water  and  the  oil,  which  at  proper  intervals  are  dis- 
charged through  suitable  drain  pipes. 

A  receiver,  unless  made  of  prohibitory  size,  can  never  act  as  a 
reservoir  for  compressed  air,  because  upon  withdrawing  air  from 


FIG.  42. — Air  Receivers. 

it,  the  pressure  falls  so  rapidly  that  even  if  of  huge  dimensions,  a 
receiver  could  supply  the  demand  only  for  a  few  minutes,  should 
the  compressor  stop  for  that  period  of  time. 

In  order  to  fill  the  legitimate  requirements  pointed  out  above, 
the  dimensions  of  a  receiver  must  conform  to  the  capacity  of  the 
compressor  and  the  discharge  pressure  of  the  air.  What  these 
dimensions  should  be  for  any  individual  installation  is  a  matter 
that  has  been  determined  largely  by  experiment. 

Compressor  manufacturers  usually  furnish  receivers  to  go  with 
a  compressor  of  given  capacity  and  list  in  their  catalogues  the 


160  COMPRESSED  AIR 

proper  size  of  a  receiver  corresponding  to  the  output  of  the 
compressor  in  cubic  feet  of  free  air  per  minute. 

Air  receivers  are  built  either  horizontal  or  vertical.  They  are 
cylindrical  vessels  made  of  sheet  steel  of  large  tensile  strength. 
The  girth  seams  are  single,  and  the  side  seams  double-riveted. 
A  manhole  is  provided  for  inspection  and  repairs. 

Each  receiver  is  usually  provided  with  a  pressure  gage,  a  safety 
valve  and  a  blow-off  cock. 

Fig.  42  shows  a  vertical  and  a  horizontal  receiver  built  by  the 
Sullivan  Machinery  Co. 

162.  After-coolers. — Inasmuch  as  they  perform  practically 
the  same  function  as  an  inter-cooler,  they  are  usually  of  the  same 
or  very  similar  construction  as  the  inter-cooler  shown  in  Fig.  39. 
They  are  sometimes  employed  in  place  of  an  ordinary  receiver 
in  order  to  realize  more  fully  the  saving  of  power  that  results 
from  the  partial  cooling  of  the  air  in  the  receiver.  Such  cooling 
reduces  the  momentary  increase  of  pressure  due  to  the  heat  of 
compression  and  as  a  consequence  diminishes  the  power  required 
in  forcing  the  air  out  of  the  compressor  cylinder  into  the  receiver. 

They  also  secure  a  more  complete  cooling  of  the  air  before  it 
enters  the  pipe  line,  and  therefore  a  more  perfect  extraction  of 
moisture  and  grease  carried  in  suspension  by  the  heated  air. 


APPENDIX. 

TABLES  I  TO  IX 


APPENDIX 


101 


SO»-.C 
OTO 


iilfcg; 


*  <j 

M   J3 

o  £ 


W  n 
a 

s 


c:  cc  ic  o  *H  i*  -f  »-^  c  -H  cr.  X  x  :c  o>  >^  »-3  L-:  L^  «  re  L.'i  ^  ic  oo  O  X  c  ^  » 


Illlilllliiiillllililllllsiili 


162 


COMPRESSED  AIR 


TABLES 

TABLE  II.— VOLUME  IN  CUBIC  FEET  OF  1  LB.  OF  AIR  AT  ATMOSPHERIC 
PRESSURE  AT  SEA  LEVEL  AND  AT   VARIOUS  TEMPERATURES 


Degrees 
Fahr. 

Volume  at  atmos.  pressure 

Degrees 
Fahr. 

Volume  at  atmos.  pressure 

Cubic  feet 
in  1  Ib. 

Comparative 
volume 

Cubic  feet 
in  1  Ib. 

Comparative 
volume 

0 

11.583 

.881 

130 

14.846 

1.130 

32 

12.387 

.943 

140 

15.100 

1.149 

40 

12.586 

.958 

150 

15.351 

.168 

50 

12.840 

.977 

160 

15.603 

.187 

62 

13.141 

.000 

170 

15.854 

.206 

70 

13.342 

.015 

180 

16.106 

.226 

80 

13.593 

.034 

200 

16.606 

.264 

90 

13.845 

.054 

210 

16.860 

.283 

100 

14.096 

.073 

212 

16.910 

.287 

110 

14.344 

.092 

220 

17.128 

.301 

120 

14.592 

'M 

APPENDIX 


163 


TABLE  III.— VOLUMES.  MEAN  PRESSURES  PER  STROKE.  AND  FINAL  TEM- 
PERATURES IN  AIR  COMPRESSION  AT  SEA  LEVEL 
(Initial  temperature  =  60°  Fahr.) 


Volume 

Volume 

Mean 
pressure 

Mean 

pressure 

Final 
tempera- 

Gage 

pressure 

Abso- 
lute 
pressure 

Atmos- 
pheres 

of  air 
isother- 
mal com- 
pression 

adia- 
batic 
com- 
pression 

per 
stroke 
isother- 
mal com- 
pression 

per 
stroke 
adiabatic 
com- 
pression 

degrees 
Fahr. 
adiabatic 
compres- 
sion 

Gage 

pressure 

0 

14.7 

1. 

1. 

1. 

0. 

0. 

60 

0 

5 

19.7 

1.34 

.7462 

.81 

4.3 

4.5 

106 

5 

10 

24.7 

1.68 

.5952 

.69 

7.62 

8.27 

145 

10 

15 

29.7 

2.02 

.495 

.606 

10.33 

11.51 

178 

15 

20 

34.7 

2.36 

.4237 

.543 

12.62 

14.4 

207 

20 

25 

39.7 

2.7 

.3703 

.494 

14.59 

17.01 

234 

25 

30 

44.7 

3.04 

.3289 

.4638 

16.34 

19.4 

255 

30 

35 

49.7 

3.381 

.2957 

.42 

17.92 

21.6 

281 

35 

40 

54.7 

3.721 

.2687 

.393 

19.32 

23.66 

302 

40 

45 

59.7 

4.061 

.2462 

.37 

20.52 

25.59 

321 

45 

50 

64.7 

4.401 

.2272 

.35 

21.79 

27.39 

339 

50 

55 

69.7 

4.741 

.2109 

.331 

22.77 

29.11 

357 

55 

60 

74.7 

5.081 

.1968 

.3144 

23.84 

30.75 

375 

60 

65 

79.7 

5.423 

.1844 

.301 

24.77 

31.69 

389 

65 

70 

84.7 

5.762 

.1735 

.288 

26. 

33.73 

405 

70 

75 

89.7 

6.102 

.1639 

.276 

26.65 

35.23 

420 

75 

80 

94.7 

6.442 

.1552 

.267 

27.33 

36.6 

432 

80 

85 

99.7 

6.782 

.1474 

.2566 

28.05 

37.94 

447 

85 

90 

104.7 

7.122 

.1404 

.248 

28.78 

39.18 

459 

90 

95 

109.7 

7.462 

.134 

.24 

29.53 

40.4 

472 

95 

100 

114.7 

7.802 

.1281 

.232 

30.07 

41.6 

485 

100 

105 

119.7 

8.142 

.1228 

.2254 

30.81 

42.78 

496 

105 

110 

124.7 

8.483 

.1178 

.2189 

31.39 

43.91 

507 

110 

115 

129.7 

8.823 

.1133 

.2129 

31.98 

44.98 

518 

115 

120 

134.7 

9.163 

.1091 

.2073 

32.54 

46.04 

529 

120 

125 

139.7 

9.503 

.1052 

.202 

33.07 

47.06 

540 

125 

130 

144.7 

9.843 

.1015 

.1969 

33.57 

48.1 

550 

130 

135 

149.7 

10.183 

.0981 

.1922 

34.05 

49.1 

560 

135 

140 

154.7 

10.523 

.095 

.1878 

34.57 

50.02 

570 

140 

145 

159.7 

10.846 

.0921 

.1837 

35.09 

51. 

580 

145 

150 

164.7 

11.204 

.0892 

.1796 

35.48 

51.89 

589 

150 

164 


COMPRESSED  AIR 


TABLE  V -THEORETICAL  HORSE-POWER  AND  FINAL  TEMPERATURES 
(Initial  temperature  =  60°  Fahr   at  sea  level) 


Single-stage 

compression 

Two-stage 

Three-stage 

Four-stage 

Iso- 

compression 

compression 

compression 

ther- 

Adiabatic 

mal 

~a  S     "a  o  !  "3 

If 

1 

•c  ~ 

ll 

"3 

"C  z 

!« 

•3 

41 

|I 

|J 

| 

1 

|1 

1 

ja  a 

|'l 

o 

5! 

x  — 

|1 

1 

11 

II 

II 

I 

H 

•21 

il 

.2 

0 

£1 

|| 

2 

fc§ 

I 

o, 
O 

Atmospheres 

iver  required  to  c 
L  cu.  ft.  free  air 

iver  required  to  ( 
1  cu.  ft.  free  air 

1 
a 

% 

temperature  deg 

wer  required  to  < 
^  cu.  ft.  free  air 

3 

perature  degrees 
oling  adiabatic  c 

wer  required  to 
L  cu.  ft.  free  ail 

1 
i 

perature  degrees 
>oling  a  diabatic 

,wer  required  to 
1  cu.  ft.  free  aii 

:y  as  compared 

i  perature  degree! 
ooling  a  diabatic 

Horse-po' 
deliver  J 

Horse-po- 
deliver 

Efficienc 

I 

ag 

I! 

s-9 

!| 

i 

Final  tem 
1  inter-c< 

^ 

e 

w 

P 

5 
10 

1.34 
1  6£ 

.0188  .01971.96 
03331  na«9.1  Q.I 

106!  .  .  . 
145i 

15 

2  0$ 

]0481 

.0505  !  .90 

178 

20 

2  3f 

0551 

'.  0630'    aa 

207 

2*  7( 

0638 

A7£ 

85 

234 

30 

3^04 

!0713|!085 

252 

40 

3.72 

.0843  .104 

'.SI 

302 

50 

4.40 

.0948  .120 

.79 

339 

'.  169' 

87  ; 

188 

60 

5.08 

.1037  .134 

.77 

375 

.121 

Mi 

203 

70 

5.76  .1120  .148 

75 

405  .131 

85 

214 

80 

6  44     1196     16 

74 

432     141 

85 

224 

90 

7'.  12k  1260  !l71 

74 

459!!l50 

84 

234 

100 

7.80  .  1320 

.  182 

73 

485:  .  158 

83 

243 

110 

8~48    1371 

192 

72 

500     165 

83 

250 

120 
130 

9!  16  .  1422 
9.84  .1467 

!202 
.210 

71 
70 

529j!l72 
560  .179 

'.S3 

.82 

257 
265 

140 

10.52  .1510 

.218 

69 

570  .  186 

.82 

272 

150 

11.201  .  1547 

226 

.69 

589    193 

81 

279 

182 

85 

200 

160 

11  !  88  !  1583 

^234 

.68 

607  !  198 

'.SI 

285 

!l87 

.85 

204 

180 

13.24  .  1656 

.249 

.67 

640  .  208 

.80 

297 

.197 

.84 

211 

200 

14  .  60     1  79n 

263 

.65 

672    217 

79 

309 

.206 

s.', 

218 

225 

16^3 

.1790 

'.278 

715  '.227 

'.79 

320 

^83 

224 

250 

18. 

.1860 

.292 

!64 

749  .237 

.78 

331 

!224 

83    230 

275 

19.7 

.1920 

.306 

.63 

780  .247 

.78 

342 

.233 

v_-    j  •;.; 

300 

21.4 

.1970 

.317 

.62 

815 

256 

.77 

352 

.241 

.82  1241 

350 

24.8 

.2060 

.342 

.60 

867 

.272 

.76 

370 

.252 

.82 

2.50 

400 

28.2 

.2140 

.364 

.59 

915 

.283 

.76 

380 

.262 

.82 

258 

450 

31.6 

.2230 

.381 

.58 

960 

.295 

.75 

397 

.272 

.82 

500 

35. 

.22901.398 

.57 

1000 

.307 

.75 

415 

.282 

.81 

27.r> 

^26' 

'.SS 

"215" 

550 

38.4 

.2340 

416 

.56 

1040 

.321 

.73 

430 

.292 

.80 

283 

.269 

.87 

220 

600 

41.8 

.240 

.432 

.55 

1077 

.332 

.72 

442 

.300 

.80 

290 

.278 

.si; 

225 

650 

45.2 

.245 

.447 

.55 

1113 

.345 

.71 

451 

.31 

.79 

2<<f> 

.J> 

.86 

228 

700 

48.6 

.249 

.461 

.54 

1136 

.355 

.70 

458 

.32 

.78 

.29 

.86 

234 

750 

52. 

.252 

.475 

.53 

1178 

.363 

.69 

462 

.327 

.78 

305 

.296 

.85 

236 

800 

55.4 

.258 

.488 

.52 

120S 

.  373 

.69 

468 

.334 

.78 

309 

::  f. 

.xr, 

240 

850 

58.8 

.262 

.500 

.52 

1237 

.381 

.69 

480 

.341 

.77    314 

.85 

244 

900 

62.2 

.265 

.512 

.52 

1265 

.388 

.68 

490 

.347 

.76    319 

!aia 

.85 

247 

950 

65.6 

.268 

.523 

.51 

1292 

.395 

.68 

495 

.354 

.76  1322 

.3161.85 

250 

1000 

69. 

.272 

.534 

.51 

131* 

.403 

.67 

498 

.360 

.75 

325 

33 

.s.-, 

252 

1100 

75.8 

.278 

.555 

.50 

1367 

.416 

.67 

507 

.370 

.75 

331 

254 

1200 

82.6 

.283 

.575 

.49 

141J 

.429 

.66 

525 

.381 

.74 

338 

.33' 

!84 

258 

1300 

89.4 

.289 

.594 

.49 

145' 

.441 

.66 

534 

.390 

.74 

342 

.341 

.84 

265 

1400 

96.2 

.293 

.611 

.48 

149* 

.452 

.65 

550 

.399 

.74 

349 

.34? 

.84 

270 

1500 

103. 

.297 

.627 

.48 

153' 

.462 

.65 

563 

.406 

.73 

353 

.35^ 

.84 

273 

1600 

109.8 

.301 

.643 

.47 

157, 

.472 

.64 

568 

.415 

.73 

358 

.361 

.83 

276 

1700 

116.6 

.305 

.659 

.47 

16K 

.482 

.63 

589 

.424 

.72 

364 

.367 

.83 

280 

1800 

123.4 

.309 

.673 

.46 

164, 

.491 

.63 

606 

.431 

.72 

370 

.375 

.83 

284 

1900 

130.2 

.313 

.(W7 

.46 

167! 

.-.00 

.63 

628 

.438 

.72 

374 

.37' 

.83 

287 

2000 

139. 

.317 

.701 

.45 

1705 

.509 

.62 

639 

.444 

.71 

378 

.381 

.83 

290 

2250 

154. 

.324 

.733 

.44 

17& 

.528 

.62 

645 

.460 

.70 

385 

.39C 

.82 

294 

2500 

171. 

.331 

.763 

.43 

185 

.547 

.61 

654 

.474 

70 

398 

40! 

.82 

Ma 

3000 

205. 

.342 

.816 

.42 

197 

.579 

.59 

670 

.500 

.69 

414 

.42 

.81 

308 

1     !       2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

APPENDIX 


165 


TABLE  IV.— VOLUME  WHICH  1  CU.  FT.  OF  FREE  AIR,  HAVING  A  TEMPERA- 
TURE OF  60°  FAHR.,  WILL  OCCUPY  WHEN  COMPRESSED  IN  ONE 
STAGE  ADIABATICALLY  TO  VARIOUS  ATMOSPHERES 

Also  final  temperature  of  the  air  at  such  pressures 


1 

2 

3 

4 

Pressure  in  atmos- 
pheres 

Absolute  pressures 
in  Ib.  per.  sq.  in. 

Volumes  in  cu.  ft. 
adiab.  comp. 

Final  temp.,  degrees 
Fahrenh. 

1.00 

14.70                               1.000 

60.0 

1.25 

18.37 

0.854 

94.8 

1.50 

22.05 

0.750 

124.9 

2.00 

29.40 

0.612 

175.8 

2.50 

36.70 

0.522 

218.3 

3.00 

44.10 

0.459 

255.1 

3.50 

51.40 

0.411 

287.8 

4.00 

58.80 

0.374 

317.4 

5.00 

73.50 

0.319 

369.4 

6.00 

88.20 

0.281 

•414.5 

7.00 

102.90 

0.252 

454.5 

8.00 

117.60 

0.229 

490.6 

9.00 

132.30 

0.211 

523.7 

10.00 

147.00 

0.195 

554.0 

15.00 

220.50 

0.147 

681.0 

TABLE  VI.— MULTIPLIERS  FOR  DETERMINING  THE  VOLUME  OF  FREE  AIR 
AT  VARIOUS  ALTITUDES  WHICH,  WHEN  COMPRESSED  TO  VARIOUS 
PRESSURES,  IS  EQUIVALENT  IN  EFFECT  TO  A  GIVEN  VOLUME  OF 
FREE  AIR  AT  SEA  LEVEL 


Barometric  pressure 


Multiplier 


Altitude 
in  feet 

Inches  of 
mercury 

Pounds  per 
square  inch 

Gage  pressure  (pounds) 

60' 

80 

100 

125     |        150 

0 

30.00 

14.75 

.000 

.000 

1.000 

.000 

.000 

1,000 

28.88 

14.20 

.032 

.033 

.034 

.035 

.036 

2,000 

27.80 

13.67 

.064 

.066 

.068 

.071 

.072 

3,000 

26.76 

13.16 

.097 

.102 

.105 

.107 

.109 

4,000 

25.76 

12.67 

.132 

.139 

.142 

.147 

.149 

5,000 

24.79 

12.20 

.168 

.178 

.182 

.187 

.190 

6,000 

23.86 

11.73 

.206 

.218 

.224 

.231 

.234 

7,000 

22.97 

11.30 

.245 

1.258 

.267 

.274 

.278 

8,000 

22.11 

10.87 

.287 

1.300 

.310 

.319 

.326 

9,000 

21.29 

10.46 

.329 

1.346 

.356 

.366 

.374 

10,000 

20.49 

10.07 

.373 

1.394 

.404 

.416 

.424 

166 


COMPRESSED  AIR 


TABLE   VII— EFFECT   OF  INITIAL  OR   IN-TAKE   TEMPERATURE   ON  EFFI- 
CIENCY AND  CAPACITY  OF  AIR  COMPRESSORS 
Unit  capacity  and  efficiency  assumed  at  60°  Fahr. 


Initial  temperature 

Relative  capacities 
and  efficiencies 

Initial  temperature 

Relative  capaci- 
ties and  effi- 
ciencies 

Degrees 
Fahr. 

Degrees 
Abs. 

Degrees 
Fahr. 

Degrees 
Aba. 

-20 

441 

.18 

70 

531 

0.980 

-10 

451 

.155 

80 

541 

0.961 

0 

461 

.13 

90 

551 

0.944 

10 

471 

.104 

100 

561 

0.928 

20 

481 

.083 

110 

571 

0.912 

30 

491 

.061 

120 

581 

0.896 

32 

493 

.058 

130 

591 

0.880 

40 

501 

.040 

140 

601 

0.866 

50 

511 

.020 

150 

611 

0.852 

60 

521 

.000 

160 

621 

0.838 

ILP.  FINAL  VOLUME  AND  FINAL  ABSOLUTE 
TEMPERATURE 


Theoretical  horse  power 


Final  volume 
in  cubic  feet 


Final  absolute 
temperature 


r,-r.(£)»-° 


.0.29 


4 
stage 


APPENDIX 


167 


B  = 

II 

So 


gt 

5^ 

S'§ 
«s 


2 

•   O   1--    »O   1C   CO   O 
•        ;         rH^HCNCOCOO 

•  d  d  d  d  d  *H 

o 

00    03 

:  d  d  d  d  d  *  rn 

CO 

•    C5   t^» 

*• 

MM;  !512!SS^5 

0 

:    :    :    :    :2il§l§^2^§ 

•OOOOO'-H'-H(NCOiC 

10 

•  co  oo 
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INDEX 


(Figures  refer  to  number  of  article) 


Absolute  pressure,  11 
temperature,  10 
zero,  9 

Adiabatic   compression   and  expan- 
sion, 14 

compression  curve,  43 
compression,    graphic    illustra- 
tion, 42 

horse  power,  47,  48,  50 
mean  gage  pressure,  46 
theory  of,  40 
work  per  stroke,  44,  45 
compression,    relation    between 
volume,  pressure  and  tem- 
perature, 41 

Advantages  of  stage  compression,  75 
After  cooler,  162 

Air  card,  single  stage  compression,  83 
two  stage  compression,  84,  85 
composition  of,  1 
compressed  in  compressors,  25, 

29 

compressors,  126 
cylinder,  25 

unloaders,  158 
cylinders,  dimensions  of,  63,  64, 

65,66 

engines,  106,  116 
indicator  card,  82,  85 
inlet  valves,  27,  144,  145,  146, 

147 

pressure  regulator,  159 
receiver,  161 
re-heaters,  123,  124,  125 
used  with  complete  expansion, 

110 

partial  expansion,  113 

weight  of,  2,  21,  23,  24,  24a 

Altitude,  compression  at,  77,  78,  79 

effect  of  on  transmission,  97 


Altitude,  effect  of  on  pipe  line  effi- 
ciency, 102 
how  calculated,  4 
multipliers  for  computation,  78 
power  required  for  compression 

at,  79 

volumetric  efficiency  at,  77,  81 
Atmospheric  pressure,  3 

how  calculated,  4 

Atmosphere,  work  performed  by  in 
compression  and  delivery, 
33,  117 
Automatic  regulators,  29,  157 

B 

Belted,  compared  with  steam  driven 

compressors,  137 
Belt  driven  compressors,  137,  138 

two  stage  compressor,  138 
Bends  in  air  pipes,  99 
Boyle's  law,  15,  16 
Boyle's  and  Charles'  laws  combined, 

20 

Branch  pipes,  dimensions  of,  98 
British  Thermal  Unit,  6 


Capacity  affected  by  intake  air,  54 

throttling  of  intake  air,  87 
of  compressor,  54 
of  compressor  affected  by  clear- 
ance, 54 

Charles'  law,  17,  18,  19 
Choking  of  air  pipes  by  ice,  104 
Clearance,  51 

effect  of  on  power  consumption, 

50,  52 
effect  of  on  volumetric  efficiency, 

50 
losses  due  to,  52 


169 


170 


INDEX 


Compound  compression,  25,  57 
advantages  of,  75 
at  altitudes,  80 
ratio  of  compression  in,  59 
when  used,  76 
Compressed  air  drills,  109 
air,  reheating  of,  122 

indicator  cards,  82,  8£ 
ah-    installation,    efficiency    of, 

121 

air  used  with  complete  expan- 
sion, 110,  111 
partial    expansion,  113,    114, 

115 
Compression  of  ah-  in  compressors, 

25,29 
work  all  converted  into    heat, 

117 

Compressor  speed,  55 
Construction  of  pipe  line,  104 
Conveyance  of  compressed  air,  91, 

105 
Cooling  of  air  during  compression, 

26,57 

water  required  in  air  compres- 
sion, 86 
Cylinder  diameters  of  compressors, 

63 

four  stage  compressor,  66 
three  stage  compressor,  65 
two  stage  compressor,  64 


Diameters  of  air  cylinders,  63,  64, 

65,66 

Dimensions  of  pipe  line,  95,  103 
Discharge  valves,  27,  148,  153 
Dry  air,  specific  heat  of,  8 
Dryer  air  in  compound  compression, 

75 
Duplex  compressors,  127 

disadvantages  of,  131a 
steam-driven  compressor,  opera- 
tion of,  131 

single  stage  compressor,  132 
two    stage    compressor,    133, 
134 


E 


Efficiency  of  air  used  at  full  pressure, 

109 

compressor  plant,  87 
pipe  line,  101,  102 
compressed  air  installation,  121 
pipe  line  affected  by  altitude, 

102 

Elbows  in  pipe  lines,  99 
Electrically  driven  compressors,  140 
geared,    two-stage    compressor, 

141 

direct-connected,  two-stage  com- 
pressor, 141,  142 
Energy  in  air  after  abstraction  of 

heat,  117 
Expansion  of  air,  adiabatic,  14 

isothermal,  13,  39 
Explosion  preventives,  90 
Explosions  due  to  throttling  devices, 

89 
in  air  compressors,  75,  88 


Final  temperature  of  compressed  air, 

41,  41a 

Flow  of  compressed  air  in  pipes,  92 
of  compressed  air  from  an  ori- 
fice, 105 

Four  stage  compressor,  cylinder  di- 
ameters, 66 

stage  compression,  ratio  of,  62 
Free  air,  12 
Freezing  of  moisture   contained   in 

compressed  air,  75e,  104 
prevented  by  re-heating,  122 
Friction  losses  in  air  compression,  50 
engines,  116 
pipes,  92 

affecting  power  con- 
sumption, 50,  56 
Fuel  cost  of  re-heating,  122 

G 

Gage  pressure,  11 
Gay  Lussac's  law,  17 
Governors,  speed,  159,  160 


INDEX 


171 


Graphical  illustration  of  isothermal 

compression,  31 
adiabatic  compression,  42 


H 


Heat  of  compression,  61 

general  effect  of  on  air,  5 

loss,  effect  of,  117 

Horse  power,  adiabatic  compression 
and  delivery,  47,  50 

of  air  engines  using  air  with  par- 
tial expansion,  115,  116 

of  four-stage  adiabatic  compres- 
sion and  delivery,  71,  74 

of  single-stage  isothermal  com- 
pression and  delivery,  37, 
50 

of  three-stage  adiabatic  com- 
pression and  delivery,  70, 74 

of  two-stage  adiabatic  compres- 
sion and  delivery,  68,  69,  74 


Indicator  cards,  82,  83,  84,  85 

Ingersoll-Rogler  valve,  147 

Inlet  valves,  27,  144,  145,  146 

Intercooler,  57,  154,  155 

Internal  or  intrinsic  energy  of  air, 
118,  119,  120 

Isothermal  compression,  13,  30,  31 
curve,  equation  of,  32 
horse  power,  37 
mean  gage  pressure,  36 
not  attainable  in  practice,  38 
work  per  stroke,  33,  34,  35 
expansion,  13,  39 
hovse  power,  39 


Joule's  law,  118 


Laidlaw-Dunn-Gordon     compressor, 

132 

Leaks  in  compressor  cylinder,  cause 
of  explosion,  88 
pipe  line,  104,  105 


Leaky  air  pistons,  effect  on  air  card, 

82 
discharge  valves,  effect  on  air 

card,  82 
inlet  valves,  effect  on  air  card, 

82 
Loss  of  capacity  due  to  throttling  of 

inlet  air,  53,  87 

of  energy  due  to  loss  of  heat,  87 
of  energy  due  to  leaks,  87 
pressure  in  pipe  line,  93 
power  in  pipe  line,  94 
due  to  clearance,  52 
volumetric    efficiency    due    to 

clearance,  52 
Losses  due  to  heating  of  intake  air, 

87,  121 
Lubrication,  26,  75 

M 

Mean  gage  pressure,  isothermal  single 
stage  compression  and  deliv- 
ery, 36 

gage  pressure,  adiabatic  single 
stage  compression  and  de- 
livery, 46 

gage  pressure,   two-stage   com- 
pression and  delivery,  72 
three-stage  compression  and  de- 
livery, 73 

at  partial  expansion,  114 
Mechanically  controlled  air  valves, 

27,  146 
Mechanical  details  of  compressors, 

143 

efficiency  of  compressor,  56,  87 
Moisture  in  air,  effect  of  on  specific 

heat,  8 

Multipliers  for  altitude  computa- 
tion, 78 

Multi-stage  compression,  25,  57 
advantages  of,  75 
at  altitudes,  80 
when  to  use,  76 

N 

"n,"  value  of,  40,   117a 
Nordberg  compressor,  141 
Norwalk  compressors,  138,  139 


172 


INDEX 


0 


Oils,  lubricating,  88,  90 


Pipe  line  construction,  104 
computation  formulas,  96 
dimensions  affected  by  altitude, 

97 

dimensions,  95,  103 
effect  of  leaks  in,  104,  105 
efficiency,  101 

affected  by  altitude,  102 
loss  of  pressure  in,  93 

power  in,  94 
Piston  displacement,  51 

speed  of  compressor,  55 
Poppet  valves,  27,  145 


Speed,  increasing  difficulty  in  lubri- 
cation, 55 
governor,  159 
Stage-compression,  57 
advantages  of,  75 
at  altitudes,  80 
increased  safety  in,  75 
when  used,  76 
ratio  of  compression  in,  59 
Steam-driven  compressors,  127,  135 
Steam  economy  in  stage  compression, 

75 
Straight-line  compressors,  127 

steam-driven     compressors, 

operation  of,  128 
single  stage  compressor,  129 
two  stage  compressor,  130 
Sullivan  compressors,  129,  130 


H 


Rating  of  compressors,  54 

Ratio   between    final    pressure   and 

power  required,  49 
of    compression    in    two-stage 

compressors,  60 
in  three-stage  compressors,  61 
in  four-stage  compressors,  62 
in  compound  compressors,  59 
Receiver  pressure,  29 
Receivers,  161 

Regulators,  automatic,  29,  157 
Re-heaters,  123,  124,  125 
Re-heating  of  compressed  air,  122 

to  increase  efficiency,  121 
Rock  drills,  109 
Rope  driven  compressor,  140 


3 


Single  stage  compression,  25,  28 

compression  air  card,  83 
Specific  heat,  6 

of  air  at  constant  volume,  7 

pressure,  8 
Speed  of  compressors,  155 

affecting  volumetric  efficiency, 
65 


Temperatures,    adiabatic    compres- 
sion and  expansion,  41 
causes  of  abnormal,  88 
in  compound  compression,  75 
Temperature  of  intake  air  affecting 
power  required  to  compress, 
54 

losses  due  to,  54,  87 
Thermal  cost  of  re-heating,  122 
Thermodynamic  laws  applied  to  air 
compression  and  expansion, 
6,  41a,  117 
Three-stage    compression,    ratio    of 

compression,  61 
cylinder  diameters,  65 
Throttling    devices    causing    explo- 
sions, 89 

Transmission  of  air  affected  by  alti- 
tude, 97 

compressed  air,  91,  105 
Two  stage  compression,  25,  57,  58, 

60 

air  card,  84,  85 
ratio  of  compression,  60 
cylinder  diameters,  64 

U 
Unloaders,  air  cylinder,  158 


INDEX 


173 


Valves  in  air  pipes,  104 
Velocity  of  air  in  pipe  line,  100 
Volumetric    efficiency    affected    by 

clearance,  52 
efficiency,  53,  87 

in  stage  compression,  53,  67,  75 
affected    by    restricted    inlet 

area,  53,  82,  87 
at  altitudes,  81 


W 


Water  jackets,  26,  57 

required  for  cooling,  86 
wheel  dri-ven  compressor,  139 

Weight  of  air,  2,  21,  22,  23,  24,  24a 


Zero,  absolute, 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 
This  book  is  DUE  on  the  last  date  stamped  below. 


•AY  2  3  1966 


•IT 


Form  L9-10m-9,'54(7413s4)444 


THE  LH'.RARY 
LX>S  ANGELES 


TJ 
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S61c 
1921 

Engineering 
Library 


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A    000316660    o 


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